%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET858-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:10:50 PM UTC 2026
% Result : Unsatisfiable 82.02s 10.91s
% Output : CNFRefutation 77.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 28
% Syntax : Number of formulae : 92 ( 25 unt; 15 def)
% Number of atoms : 221 ( 11 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 215 ( 86 ~; 114 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 16 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f264,axiom,
! [V_n] : ~ c_less(V_n,V_n,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f310,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1358,axiom,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1359,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/sandbox/benchmark/theBenchmark.p') ).
fof(f1360,axiom,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(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/sandbox/benchmark/theBenchmark.p') ).
fof(f1361,axiom,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(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/sandbox/benchmark/theBenchmark.p') ).
fof(f1362,axiom,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
| ~ 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/sandbox/benchmark/theBenchmark.p') ).
fof(f1363,axiom,
! [V_m,V_S,T_a,V_n] :
( c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(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/sandbox/benchmark/theBenchmark.p') ).
fof(f1364,axiom,
! [V_U,V_S,T_a,V_m] :
( V_U = V_m
| c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f1366,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1367,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1368,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1731,plain,
! [X0] : ~ c_less(X0,X0,tc_nat),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f1787,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f310]) ).
fof(f2844,plain,
! [V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ! [V_B] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f1358]) ).
fof(f2845,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X0,X3,tc_set(X2))
| ~ c_lessequals(X3,X1,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f2844]) ).
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)],[f1359]) ).
fof(f2847,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2),c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(thm)],[f1360]) ).
fof(f2848,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2),X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(thm)],[f1361]) ).
fof(f2849,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| X0 != c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) ),
inference(cnf_transformation,[status(thm)],[f1362]) ).
fof(f2850,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X2),X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[status(thm)],[f1363]) ).
fof(f2851,plain,
! [V_U,V_m] :
( V_U = V_m
| ! [V_S,T_a] :
( c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ),
inference(miniscoping,[status(thm)],[f1364]) ).
fof(f2852,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| X0 = X3
| ~ c_lessequals(X0,X3,tc_set(tc_set(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)],[f2851]) ).
fof(f2853,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(f2854,plain,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1366]) ).
fof(f2855,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1367]) ).
fof(f2856,plain,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1368]) ).
fof(f2962,definition,
( sQ12_spl
<=> c_emptyset = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f2964,plain,
( sQ12_spl
| c_emptyset != c_emptyset ),
inference(component_clause,[status(thm)],[f2962]) ).
fof(f3092,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X1,X3,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2))) ),
inference(resolution,[status(thm)],[f2846,f2845]) ).
fof(f3257,definition,
( sQ30_spl
<=> c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f3259,plain,
( sQ30_spl
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3257]) ).
fof(f3306,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3259,f2854]) ).
fof(f3307,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f3306]) ).
fof(f3513,definition,
( sQ54_spl
<=> c_less(c_List_Olist_ONil,c_List_Olist_ONil,tc_nat) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f3514,plain,
( ~ sQ54_spl
| c_less(c_List_Olist_ONil,c_List_Olist_ONil,tc_nat) ),
inference(component_clause,[status(thm)],[f3513]) ).
fof(f3558,definition,
! [X0] :
( sQ61_spl
<=> ( c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f3559,plain,
! [X0] :
( ~ sQ61_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3558]) ).
fof(f3561,definition,
( sQ62_spl
<=> v_n = c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f3579,definition,
( sQ64_spl
<=> c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f3581,plain,
( sQ64_spl
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3579]) ).
fof(f3582,definition,
( sQ65_spl
<=> c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f3584,plain,
( sQ65_spl
| ~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3582]) ).
fof(f3587,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3581,f2853]) ).
fof(f3588,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f3587]) ).
fof(f3683,definition,
( sQ70_spl
<=> c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f3685,plain,
( sQ70_spl
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3683]) ).
fof(f3938,definition,
( sQ85_spl
<=> c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f3939,plain,
( ~ sQ85_spl
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f3938]) ).
fof(f3950,plain,
( ~ sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3939,f2855]) ).
fof(f3951,plain,
~ sQ85_spl,
inference(contradiction_clause,[status(thm)],[f3950]) ).
fof(f4308,definition,
( sQ95_spl
<=> c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f4310,plain,
( sQ95_spl
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f4308]) ).
fof(f4320,plain,
! [X0] :
( sQ95_spl
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f4310,f2848]) ).
fof(f4321,plain,
( sQ95_spl
| ~ sQ30_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f4320,f3558,f3257,f4308]) ).
fof(f4343,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| X0 = v_n
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f2852,f2854]) ).
fof(f4359,definition,
( sQ97_spl
<=> c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f4361,plain,
( sQ97_spl
| ~ c_lessequals(v_m,c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f4359]) ).
fof(f4363,plain,
( sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4361,f2846]) ).
fof(f4364,plain,
sQ97_spl,
inference(contradiction_clause,[status(thm)],[f4363]) ).
fof(f4389,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| v_n = c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) ),
inference(resolution,[status(thm)],[f4343,f2850]) ).
fof(f4399,plain,
( sQ61_spl
| ~ sQ30_spl
| ~ sQ95_spl
| ~ sQ70_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f4389,f3561,f3683,f4308,f3257,f3558]) ).
fof(f4503,plain,
( sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2964]) ).
fof(f4504,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f4503]) ).
fof(f4570,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3584,f1787]) ).
fof(f4571,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f4570]) ).
fof(f4944,definition,
( sQ113_spl
<=> c_lessequals(c_Datatype_Ooption_ONone,c_Datatype_Ooption_ONone,tc_set(c_Datatype_Ooption_ONone)) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f4946,plain,
( sQ113_spl
| ~ c_lessequals(c_Datatype_Ooption_ONone,c_Datatype_Ooption_ONone,tc_set(c_Datatype_Ooption_ONone)) ),
inference(component_clause,[status(thm)],[f4944]) ).
fof(f4992,plain,
( sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4946,f1787]) ).
fof(f4993,plain,
sQ113_spl,
inference(contradiction_clause,[status(thm)],[f4992]) ).
fof(f5138,plain,
( ~ sQ61_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f3559,f2856]) ).
fof(f5176,definition,
( sQ132_spl
<=> c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f5177,plain,
( ~ sQ132_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f5176]) ).
fof(f5179,plain,
( ~ sQ61_spl
| sQ132_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f5138,f3579,f5176,f3558]) ).
fof(f5254,plain,
( ~ sQ132_spl
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f5177,f3092]) ).
fof(f5266,plain,
( ~ sQ132_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f5254,f3938,f5176]) ).
fof(f5570,definition,
( sQ160_spl
<=> c_lessequals(v_n,c_Zorn_Osucc(c_Datatype_Ooption_ONone,v_n,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f5572,plain,
( sQ160_spl
| ~ c_lessequals(v_n,c_Zorn_Osucc(c_Datatype_Ooption_ONone,v_n,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f5570]) ).
fof(f5575,plain,
( sQ160_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5572,f2846]) ).
fof(f5576,plain,
sQ160_spl,
inference(contradiction_clause,[status(thm)],[f5575]) ).
fof(f6157,plain,
! [X0] :
( sQ70_spl
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f3685,f2847]) ).
fof(f6158,plain,
( sQ70_spl
| ~ sQ30_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f6157,f3558,f3257,f3683]) ).
fof(f6496,plain,
( ~ sQ54_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3514,f1731]) ).
fof(f6500,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f6496]) ).
fof(f6954,definition,
( sQ235_spl
<=> c_lessequals(c_emptyset,c_emptyset,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f6956,plain,
( sQ235_spl
| ~ c_lessequals(c_emptyset,c_emptyset,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f6954]) ).
fof(f6973,plain,
( sQ235_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6956,f1787]) ).
fof(f6974,plain,
sQ235_spl,
inference(contradiction_clause,[status(thm)],[f6973]) ).
fof(f8186,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| v_n != c_Zorn_OTFin__linear__lemma1__1(v_S,v_n,t_a) ),
inference(resolution,[status(thm)],[f2849,f2854]) ).
fof(f8206,plain,
( sQ61_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f8186,f3561,f3558]) ).
fof(f8210,plain,
$false,
inference(sat_refutation,[status(thm)],[f3307,f3588,f3951,f4321,f4364,f4399,f4504,f4571,f4993,f5179,f5266,f5576,f6158,f6500,f6974,f8206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET858-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:41:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 82.02/10.91 % Refutation found
% 82.02/10.91 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 82.02/10.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.33/11.02 % Elapsed time: 10.641617 seconds
% 4.33/11.02 % CPU time: 83.299160 seconds
% 4.33/11.02 % Total memory used: 427.443 MB
% 4.33/11.02 % Net memory used: 390.516 MB
%------------------------------------------------------------------------------