%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 21
% Syntax : Number of formulae : 76 ( 20 unt; 7 def)
% Number of atoms : 218 ( 9 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 247 ( 105 ~; 135 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 108 ( 108 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,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(f5,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(f6,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(f7,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(f8,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(f9,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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(f11,negated_conjecture,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [V_V,V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(V_V,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_V,V_U,tc_set(tc_set(t_a)))
| V_V = V_U
| c_lessequals(c_Zorn_Osucc(v_S,V_V,t_a),V_U,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [V_c,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ! [V_A] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1,X2] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( 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(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),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)],[f5]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,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)],[f6]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| ~ 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)],[f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,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_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)],[f8]) ).
fof(f24,plain,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
c_in(v_x,v_Y,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
~ c_lessequals(v_x,v_n,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_x,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f29,plain,
! [V_U] :
( ~ c_in(V_U,v_Y,tc_set(tc_set(t_a)))
| ! [V_V] :
( ~ c_in(V_V,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_V,V_U,tc_set(tc_set(t_a)))
| V_V = V_U
| c_lessequals(c_Zorn_Osucc(v_S,V_V,t_a),V_U,tc_set(tc_set(t_a))) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f30,plain,
! [X0,X1] :
( ~ c_in(X1,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(t_a)))
| X0 = X1
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
( ~ c_in(v_x,v_Y,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(v_n,v_x,tc_set(tc_set(t_a)))
| v_n = v_x ),
inference(resolution,[status(thm)],[f30,f28]) ).
fof(f32,definition,
( sQ0_spl
<=> v_n = v_x ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( ~ sQ0_spl
| v_n = v_x ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,definition,
( sQ1_spl
<=> c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f38,definition,
( sQ2_spl
<=> c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( sQ2_spl
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ3_spl
<=> c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ3_spl
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f32,f35,f38,f41]) ).
fof(f45,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f26]) ).
fof(f46,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f45]) ).
fof(f47,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f25]) ).
fof(f48,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ sQ0_spl
| ~ c_lessequals(v_n,v_n,tc_set(tc_set(t_a))) ),
inference(backward_demodulation,[status(thm)],[f33,f27]) ).
fof(f66,plain,
! [X0,X1] :
( c_lessequals(X0,X0,tc_set(X1))
| c_lessequals(X0,X0,tc_set(X1)) ),
inference(resolution,[status(thm)],[f18,f17]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X3,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X3,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f68,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(duplicate_literals_removal,[status(thm)],[f66]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_lessequals(X4,X3,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X4,X2)
| ~ c_lessequals(X3,X1,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f67,f16]) ).
fof(f75,definition,
( sQ7_spl
<=> c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( sQ7_spl
| ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f87,plain,
! [X0] :
( sQ7_spl
| ~ c_lessequals(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a))))
| ~ c_in(v_x,X0,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f77,f16]) ).
fof(f88,plain,
( sQ7_spl
| ~ c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) ),
inference(resolution,[status(thm)],[f87,f26]) ).
fof(f90,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f24]) ).
fof(f91,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X0,X3,tc_set(X2))
| ~ c_lessequals(X3,X1,tc_set(X2))
| c_lessequals(X0,X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f70,f17]) ).
fof(f94,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(duplicate_literals_removal,[status(thm)],[f92]) ).
fof(f95,plain,
! [X0] :
( ~ c_lessequals(v_x,X0,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_n,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f94,f27]) ).
fof(f99,plain,
! [X0] : ~ c_lessequals(c_Zorn_Osucc(X0,v_x,t_a),v_n,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[f95,f19]) ).
fof(f112,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f68]) ).
fof(f113,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f112]) ).
fof(f179,plain,
! [X0,X1] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),X0,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a) = X0
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,X0,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f23,f30]) ).
fof(f182,plain,
! [X0,X1] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,X0,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f22]) ).
fof(f185,plain,
! [X0,X1] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X0,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,X0,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(forward_subsumption_resolution,[status(thm)],[f182,f21]) ).
fof(f186,plain,
! [X0,X1,X2] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X2,tc_set(tc_set(t_a)))
| c_lessequals(X2,X0,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,X0,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f185,f20]) ).
fof(f188,plain,
! [X0,X1,X2] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X2,tc_set(tc_set(t_a)))
| c_lessequals(X2,X0,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,X0,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(duplicate_literals_removal,[status(thm)],[f186]) ).
fof(f196,plain,
! [X0,X1] :
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,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_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f188,f26]) ).
fof(f198,definition,
! [X0] :
( sQ20_spl
<=> ( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,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,[sQ20_spl])],[split_symbol_definition]) ).
fof(f199,plain,
! [X0] :
( ~ sQ20_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X0,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_x,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)],[f198]) ).
fof(f201,plain,
( sQ20_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f196,f75,f198]) ).
fof(f399,plain,
( ~ sQ20_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f199,f25]) ).
fof(f408,definition,
( sQ37_spl
<=> c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ37_spl
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f411,plain,
( ~ sQ20_spl
| sQ37_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f399,f35,f408,f198]) ).
fof(f412,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f99]) ).
fof(f413,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f46,f48,f91,f113,f201,f411,f413]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET857-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.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 05:44:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.46 % Refutation found
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.124771 seconds
% 0.14/0.50 % CPU time: 0.700067 seconds
% 0.14/0.50 % Total memory used: 96.056 MB
% 0.14/0.50 % Net memory used: 94.313 MB
%------------------------------------------------------------------------------