%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET863-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 : Sun Sep 27 08:31:13 AM UTC 2026
% Result : Unsatisfiable 5.67s 3.38s
% Output : Refutation 6.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 476 ( 34 ~; 38 |; 0 &; 404 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 62 ( 0 ^; 62 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_c_decl,type,
v_c: $i ).
thf(c_Zorn_Omaxchain_decl,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(v_S_decl,type,
v_S: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_Zorn_Ochain_decl,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_y_decl,type,
v_y: $i ).
thf(v_xa_decl,type,
v_xa: $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_Zorn_Ochain__extend__1_decl,type,
c_Zorn_Ochain__extend__1: $i > $i > $i > $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(c_emptyset_decl,type,
c_emptyset: $i ).
thf(c_Zorn_Omaxchain__super__lemma__1_decl,type,
c_Zorn_Omaxchain__super__lemma__1: $i > $i > $i > $i ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,negated_conjecture,
t_a @ tc_set @ ( v_S @ ( v_x @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(20,plain,
t_a @ tc_set @ ( v_S @ ( v_x @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_c @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(18,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Ochain ) @ ( v_c @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Omaxchain ) @ ( v_c @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(16,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Omaxchain ) @ ( v_c @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
t_a @ ( v_x @ ( v_xa @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(15,plain,
t_a @ ( v_x @ ( v_xa @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,negated_conjecture,
t_a @ tc_set @ ( v_x @ ( v_y @ c_lessequals ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(21,plain,
t_a @ tc_set @ ( v_x @ ( v_y @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,negated_conjecture,
~ ( t_a @ ( v_y @ ( v_xa @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(17,plain,
~ ( t_a @ ( v_y @ ( v_xa @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ ( A @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_in ) ) )
| ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
thf(34,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_in ) ) )
| ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( F @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
thf(36,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( F @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( F @ ( C @ ( F @ ( D @ c_Zorn_Omaxchain__super__lemma__1 ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( B @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( E @ c_Zorn_Omaxchain ) @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ( C @ tc_set @ ( D @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( C @ tc_set @ ( D @ ( C @ tc_set @ ( c_emptyset @ ( A @ c_insert ) ) @ c_union ) ) @ c_in ) ) )
| ( C @ tc_set @ ( D @ ( C @ ( A @ ( D @ c_Zorn_Ochain__extend__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_c @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_y @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(19,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_c @ ( A @ c_in ) ) )
| ( t_a @ tc_set @ ( v_y @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[24,20,18,16,26,15,28,21,17,32,34,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET863-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n004.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 08:22:51 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.27/1.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.65/1.46 % [INFO] Parsing done (188ms).
% 1.65/1.48 % [INFO] Running in sequential loop mode.
% 2.83/2.07 % [INFO] eprover registered as external prover.
% 2.83/2.08 % [INFO] Scanning for conjecture ...
% 3.10/2.24 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 3.10/2.30 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 3.27/2.35 % [INFO] Problem is propositional (TPTP CNF).
% 3.27/2.35 % [INFO] Type checking passed.
% 3.27/2.36 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.67/3.38 % External prover 'e' found a proof!
% 5.67/3.38 % [INFO] Killing All external provers ...
% 5.67/3.38 % Time passed: 2758ms (effective reasoning time: 1897ms)
% 5.67/3.38 % Axioms used in derivation (7): cls_Set_OsubsetI_1, cls_Zorn_Ochain__extend_0, cls_Zorn_Omaxchain__super__lemma_0, cls_Set_OsubsetI_0, cls_Set_OsubsetD_0, cls_Zorn_Omaxchain__super__lemma_1, cls_Zorn_Ochain__extend_1
% 5.67/3.38 % No. of inferences in proof: 29
% 5.67/3.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2758 ms resp. 1897 ms w/o parsing
% 6.01/3.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.01/3.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------