%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:31:11 AM UTC 2026
% Result : Unsatisfiable 5.07s 2.67s
% Output : Refutation 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 500 ( 34 ~; 44 |; 0 &; 422 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_m_decl,type,
v_m: $i ).
thf(c_Zorn_OTFin_decl,type,
c_Zorn_OTFin: $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(v_n_decl,type,
v_n: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Zorn_Osucc_decl,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(c_Zorn_OTFin__linear__lemma1__1_decl,type,
c_Zorn_OTFin__linear__lemma1__1: $i > $i > $i > $i ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,negated_conjecture,
~ ( t_a @ tc_set @ tc_set @ ( v_m @ ( v_n @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(14,plain,
~ ( t_a @ tc_set @ tc_set @ ( v_m @ ( v_n @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] : ( C @ tc_set @ tc_set @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_n @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(13,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_n @ 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_OTFin ) @ ( v_m @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,plain,
t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ ( v_m @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,negated_conjecture,
~ ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_m @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(15,plain,
~ ( t_a @ tc_set @ tc_set @ ( v_n @ ( v_m @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( A @ ( C @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( A @ ( C @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( D @ ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ ( A @ ( B @ c_Zorn_OTFin__linear__lemma1__1 ) ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( D @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[25,14,20,13,12,18,23,30,15,28,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.25/0.49 % Computer : n001.cluster.edu
% 0.25/0.49 % Model : x86_64 x86_64
% 0.25/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.49 % Memory : 8046.5625MB
% 0.25/0.49 % OS : Linux 6.8.0-71-generic
% 0.25/0.49 % CPULimit : 300
% 0.25/0.49 % WCLimit : 300
% 0.25/0.49 % DateTime : Sat Sep 26 08:28:28 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.00/1.04 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.24 % [INFO] Parsing done (191ms).
% 1.58/1.25 % [INFO] Running in sequential loop mode.
% 2.48/1.62 % [INFO] eprover registered as external prover.
% 2.48/1.63 % [INFO] Scanning for conjecture ...
% 2.70/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.70/1.73 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.70/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.70/1.78 % [INFO] Type checking passed.
% 2.70/1.78 % [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 ...
% 5.07/2.66 % External prover 'e' found a proof!
% 5.07/2.66 % [INFO] Killing All external provers ...
% 5.07/2.66 % Time passed: 2012ms (effective reasoning time: 1408ms)
% 5.07/2.66 % Axioms used in derivation (7): cls_Zorn_OTFin__linear__lemma1_0, cls_Zorn_OTFin__linear__lemma1_3, cls_Set_Osubset__trans_0, cls_Zorn_OTFin__linear__lemma1_2, cls_Zorn_OAbrial__axiom1_0, cls_Zorn_OTFin__linear__lemma2_0, cls_Zorn_OTFin__linear__lemma1_1
% 5.07/2.66 % No. of inferences in proof: 23
% 5.07/2.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2012 ms resp. 1408 ms w/o parsing
% 5.48/2.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.48/2.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------