%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET852-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 10 unt; 4 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 69 ( 28 ~; 37 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1358,axiom,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1359,axiom,
! [V_A,V_B,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1360,axiom,
! [V_B,V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1364,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1365,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1366,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),V_U,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2843,plain,
! [V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| ! [V_B] :
( c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| c_in(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_C,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1358]) ).
fof(f2844,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3)) ),
inference(cnf_transformation,[status(thm)],[f2843]) ).
fof(f2845,plain,
! [V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| ! [V_B] :
( c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),V_A,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1359]) ).
fof(f2846,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3)) ),
inference(cnf_transformation,[status(thm)],[f2845]) ).
fof(f2847,plain,
! [V_A,V_C,T_a] :
( c_lessequals(c_Union(V_C,T_a),V_A,tc_set(T_a))
| ! [V_B] :
( c_lessequals(V_B,c_Union(V_C,T_a),tc_set(T_a))
| ~ c_lessequals(V_B,c_Zorn_OUnion__lemma0__1(V_A,V_B,V_C,T_a),tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1360]) ).
fof(f2848,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Union(X2,X3),X1,tc_set(X3))
| c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3)) ),
inference(cnf_transformation,[status(thm)],[f2847]) ).
fof(f2853,plain,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1364]) ).
fof(f2854,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1365]) ).
fof(f2855,plain,
! [X0] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(thm)],[f1366]) ).
fof(f2867,definition,
( sQ0_spl
<=> c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f2868,plain,
( ~ sQ0_spl
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f2867]) ).
fof(f2874,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2868,f2853]) ).
fof(f2875,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f2874]) ).
fof(f3013,plain,
! [X0] :
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f2846,f2854]) ).
fof(f3016,plain,
! [X0] :
( c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X0,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f2848,f2854]) ).
fof(f3031,plain,
~ c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[f3013,f2853]) ).
fof(f3033,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[f3016,f2853]) ).
fof(f3062,plain,
( ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f3033,f2855]) ).
fof(f3063,definition,
( sQ30_spl
<=> c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f3064,plain,
( ~ sQ30_spl
| c_lessequals(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3063]) ).
fof(f3066,definition,
( sQ31_spl
<=> c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f3068,plain,
( sQ31_spl
| ~ c_in(c_Zorn_OUnion__lemma0__1(v_m,c_Zorn_Osucc(v_S,v_m,t_a),v_Y,tc_set(t_a)),v_Y,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3066]) ).
fof(f3069,plain,
( ~ sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f3062,f3063,f3066]) ).
fof(f3070,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3064,f3031]) ).
fof(f3071,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f3070]) ).
fof(f3072,plain,
( sQ31_spl
| c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f3068,f2844]) ).
fof(f3079,definition,
( sQ32_spl
<=> c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f3080,plain,
( ~ sQ32_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3079]) ).
fof(f3082,plain,
( sQ31_spl
| sQ0_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f3072,f3079,f2867,f3066]) ).
fof(f3083,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3080,f2854]) ).
fof(f3084,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f3083]) ).
fof(f3085,plain,
$false,
inference(sat_refutation,[status(thm)],[f2875,f3069,f3071,f3082,f3084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET852-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n003.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:43:15 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.48 % Refutation found
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.50 % Elapsed time: 0.149179 seconds
% 0.12/0.50 % CPU time: 0.667585 seconds
% 0.12/0.50 % Total memory used: 161.561 MB
% 0.12/0.50 % Net memory used: 160.917 MB
%------------------------------------------------------------------------------