%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 43 ( 13 unt; 2 def)
% Number of atoms : 132 ( 9 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 154 ( 65 ~; 87 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 91 ( 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(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_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/sandbox2/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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f16,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)],[f5]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,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)],[f7]) ).
fof(f20,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)],[f8]) ).
fof(f21,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)],[f9]) ).
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_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)],[f10]) ).
fof(f23,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)],[f11]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ 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)],[f23]) ).
fof(f25,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)],[f18,f17]) ).
fof(f221,plain,
! [X0,X1,X2,X3] :
( c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) = X0
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),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_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,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(resolution,[status(thm)],[f22,f24]) ).
fof(f224,plain,
! [X0,X1,X2,X3] :
( c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) = X0
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),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_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,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(duplicate_literals_removal,[status(thm)],[f221]) ).
fof(f225,plain,
! [X0,X1,X2,X3] :
( c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) = X0
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,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(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(forward_subsumption_resolution,[status(thm)],[f224,f19]) ).
fof(f226,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(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(backward_subsumption_resolution,[status(thm)],[f21,f227]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) = X0
| 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(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(forward_subsumption_resolution,[status(thm)],[f225,f20]) ).
fof(f253,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X0,X3,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(resolution,[status(thm)],[f226,f25]) ).
fof(f255,plain,
! [X0] :
( c_lessequals(X0,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,X0,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)],[f253,f13]) ).
fof(f258,plain,
( c_lessequals(v_m,v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[f255,f12]) ).
fof(f263,definition,
( sQ1_spl
<=> c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ1_spl
| c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ2_spl
<=> c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ2_spl
| c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( sQ2_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f258,f263,f266]) ).
fof(f270,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f14]) ).
fof(f271,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f272,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f15]) ).
fof(f273,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f272]) ).
fof(f274,plain,
$false,
inference(sat_refutation,[status(thm)],[f269,f271,f273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:42:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.44 % Elapsed time: 0.073902 seconds
% 0.11/0.44 % CPU time: 0.299728 seconds
% 0.11/0.44 % Total memory used: 85.366 MB
% 0.11/0.44 % Net memory used: 84.550 MB
%------------------------------------------------------------------------------