%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET844-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 02:10:47 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 13 unt; 3 def)
% Number of atoms : 69 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 68 ( 34 ~; 31 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f310,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1361,axiom,
! [V_x,V_S,T_a] : c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1363,axiom,
! [V_Y,V_S,T_a] :
( c_in(c_Union(V_Y,tc_set(T_a)),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_Y,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1364,axiom,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1365,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1366,negated_conjecture,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1367,negated_conjecture,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1784,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(f1785,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)],[f1784]) ).
fof(f1786,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f310]) ).
fof(f2846,plain,
! [X0,X1,X2] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(thm)],[f1361]) ).
fof(f2848,plain,
! [X0,X1,X2] :
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
inference(cnf_transformation,[status(thm)],[f1363]) ).
fof(f2849,plain,
! [V_m,T_a,V_n] :
( c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ! [V_S] :
( V_m != c_Zorn_Osucc(V_S,V_m,T_a)
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(miniscoping,[status(thm)],[f1364]) ).
fof(f2850,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| X0 != c_Zorn_Osucc(X1,X0,X2)
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(thm)],[f2849]) ).
fof(f2851,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1365]) ).
fof(f2852,plain,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
inference(cnf_transformation,[status(thm)],[f1366]) ).
fof(f2853,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1367]) ).
fof(f2859,plain,
! [X0,X1,X2] :
( X1 = c_Zorn_Osucc(X0,X1,X2)
| ~ c_lessequals(c_Zorn_Osucc(X0,X1,X2),X1,tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[f1785,f2846]) ).
fof(f2865,definition,
( sQ0_spl
<=> c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f2867,plain,
( sQ0_spl
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f2865]) ).
fof(f2875,plain,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) ),
inference(paramodulation,[status(thm)],[f2852,f2859]) ).
fof(f2876,definition,
( sQ1_spl
<=> c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f2878,plain,
( sQ1_spl
| ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f2876]) ).
fof(f2879,definition,
( sQ2_spl
<=> v_m = c_Zorn_Osucc(v_S,v_m,t_a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2882,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f2875,f2876,f2879]) ).
fof(f2883,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2878,f1786]) ).
fof(f2884,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f2883]) ).
fof(f2885,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2))))
| c_lessequals(c_Union(X3,tc_set(X2)),X0,tc_set(tc_set(X2)))
| X0 != c_Zorn_Osucc(X1,X0,X2)
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[f2850,f2848]) ).
fof(f2895,plain,
! [X0] :
( ~ c_lessequals(c_Zorn_OTFin(v_S,t_a),c_Zorn_OTFin(X0,t_a),tc_set(tc_set(tc_set(t_a))))
| v_m != c_Zorn_Osucc(X0,v_m,t_a)
| ~ c_in(v_m,c_Zorn_OTFin(X0,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f2885,f2853]) ).
fof(f2926,plain,
( v_m != c_Zorn_Osucc(v_S,v_m,t_a)
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f2895,f1786]) ).
fof(f2927,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f2926,f2865,f2879]) ).
fof(f2928,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2867,f2851]) ).
fof(f2929,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f2928]) ).
fof(f2930,plain,
$false,
inference(sat_refutation,[status(thm)],[f2882,f2884,f2927,f2929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET844-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:40:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.40 % Drodi V4.1.1
% 0.13/0.44 % Refutation found
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.48 % Elapsed time: 0.120152 seconds
% 0.18/0.48 % CPU time: 0.291172 seconds
% 0.18/0.48 % Total memory used: 152.167 MB
% 0.18/0.48 % Net memory used: 151.756 MB
%------------------------------------------------------------------------------