%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET848-2 : 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 : 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 : Sun Sep 27 08:31:08 AM UTC 2026
% Result : Unsatisfiable 3.64s 2.30s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 206 ( 12 ~; 10 |; 0 &; 184 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 0 ^; 30 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Union_decl,type,
c_Union: $i > $i > $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(c_Zorn_Omaxchain_decl,type,
c_Zorn_Omaxchain: $i > $i > $i ).
thf(c_Zorn_Osucc_decl,type,
c_Zorn_Osucc: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Zorn_Ochain_decl,type,
c_Zorn_Ochain: $i > $i > $i ).
thf(4,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(14,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(2,negated_conjecture,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) @ ( v_S @ c_Zorn_Osucc ) ) )
= ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,plain,
( ( t_a @ ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) @ ( v_S @ c_Zorn_Osucc ) ) )
= ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( A @ 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__chain__lemma4_0) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Ochain ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
thf(12,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( D @ ( B @ c_minus ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Omaxchain ) @ ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(8,plain,
~ ( t_a @ tc_set @ tc_set @ ( t_a @ ( v_S @ c_Zorn_Omaxchain ) @ ( t_a @ tc_set @ ( t_a @ ( v_S @ c_Zorn_OTFin ) @ c_Union ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ tc_set @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Omaxchain ) @ ( C @ ( B @ c_Zorn_Ochain ) @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ c_Zorn_Osucc ) ) )
!= A )
| ~ ( C @ tc_set @ tc_set @ ( C @ tc_set @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_Omaxchain ) @ ( C @ ( B @ c_Zorn_Ochain ) @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ tc_set @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( C @ tc_set @ ( A @ c_Union ) @ c_in ) ) )
| ~ ( C @ tc_set @ tc_set @ tc_set @ ( C @ ( B @ c_Zorn_OTFin ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[14,9,17,12,8,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET848-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.13/0.40 % Computer : n008.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 08:21:54 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.18 % [INFO] Parsing done (190ms).
% 1.28/1.19 % [INFO] Running in sequential loop mode.
% 1.89/1.59 % [INFO] eprover registered as external prover.
% 2.08/1.60 % [INFO] Scanning for conjecture ...
% 2.26/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.26/1.73 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.26/1.75 % [INFO] Problem is propositional (TPTP CNF).
% 2.26/1.75 % [INFO] Type checking passed.
% 2.26/1.76 % [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 ...
% 3.64/2.30 % External prover 'e' found a proof!
% 3.64/2.30 % [INFO] Killing All external provers ...
% 3.64/2.30 % Time passed: 1755ms (effective reasoning time: 1105ms)
% 3.64/2.30 % Axioms used in derivation (5): cls_Set_Osubset__refl_0, cls_Zorn_Osucc__not__equals_0, cls_Set_ODiffI_0, cls_Zorn_OTFin__UnionI_0, cls_Zorn_OTFin__chain__lemma4_0
% 3.64/2.30 % No. of inferences in proof: 15
% 3.64/2.30 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1755 ms resp. 1105 ms w/o parsing
% 3.64/2.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.64/2.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------