%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT388+4 : TPTP v9.3.1. Released v4.0.0.
% 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 : n002.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 07:47:38 AM UTC 2026
% Result : Theorem 10.32s 4.22s
% Output : Refutation 10.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 125 ( 6 equ; 0 cnn)
% Maximal formula atoms : 25 ( 7 avg)
% Number of connectives : 408 ( 30 ~; 33 |; 51 &; 272 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 3 ^; 26 !; 5 ?; 37 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(aUpperBoundOfIn0_decl,type,
aUpperBoundOfIn0: $i > $i > $i > $o ).
thf(aSupremumOfIn0_decl,type,
aSupremumOfIn0: $i > $i > $i > $o ).
thf(szDzozmdt0_decl,type,
szDzozmdt0: $i > $i ).
thf(aFixedPointOf0_decl,type,
aFixedPointOf0: $i > $i > $o ).
thf(sdtlpdtrp0_decl,type,
sdtlpdtrp0: $i > $i > $i ).
thf(xS_decl,type,
xS: $i ).
thf(xT_decl,type,
xT: $i ).
thf(xf_decl,type,
xf: $i ).
thf(xp_decl,type,
xp: $i ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( ( xS @ ( xT @ ( B @ aUpperBoundOfIn0 ) ) )
& ! [C: $i] :
( ( xT @ ( C @ aElementOf0 ) )
=> ( B @ ( C @ sdtlseqdt0 ) ) )
& ( xS @ ( B @ aElementOf0 ) ) )
=> ( B @ ( A @ sdtlseqdt0 ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) ) ) ) ).
thf(28,axiom,
( ( xS @ ( xT @ ( xp @ aSupremumOfIn0 ) ) )
& ! [A: $i] :
( ( ( xS @ ( xT @ ( A @ aUpperBoundOfIn0 ) ) )
| ( ! [B: $i] :
( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) )
=> ( A @ ( xp @ sdtlseqdt0 ) ) )
& ( xS @ ( xT @ ( xp @ aUpperBoundOfIn0 ) ) )
& ! [A: $i] :
( ( xT @ ( A @ aElementOf0 ) )
=> ( xp @ ( A @ sdtlseqdt0 ) ) )
& ( xf @ ( xp @ aFixedPointOf0 ) )
& ( ( xp @ ( xf @ sdtlpdtrp0 ) )
= xp )
& ( xf @ szDzozmdt0 @ ( xp @ aElementOf0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1330) ).
thf(232,plain,
( ( xS @ ( xT @ ( xp @ aSupremumOfIn0 ) ) )
& ! [A: $i] :
( ( ( xS @ ( xT @ ( A @ aUpperBoundOfIn0 ) ) )
| ( ! [B: $i] :
( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) )
=> ( A @ ( xp @ sdtlseqdt0 ) ) )
& ( xS @ ( xT @ ( xp @ aUpperBoundOfIn0 ) ) )
& ! [A: $i] :
( ( xT @ ( A @ aElementOf0 ) )
=> ( xp @ ( A @ sdtlseqdt0 ) ) )
& ( xf @ ( xp @ aFixedPointOf0 ) )
& ( ( xp @ ( xf @ sdtlpdtrp0 ) )
= xp )
& ( xf @ szDzozmdt0 @ ( xp @ aElementOf0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( xS @ ( xT @ ( xp @ aSupremumOfIn0 ) ) )
& ( ( B @ ( xp @ sdtlseqdt0 ) )
| ~ ( xS @ ( xT @ ( B @ aUpperBoundOfIn0 ) ) ) )
& ( ( B @ ( xp @ sdtlseqdt0 ) )
| ~ ( B @ ( B @ sk22 @ sdtlseqdt0 ) )
| ~ ( xS @ ( B @ aElementOf0 ) ) )
& ( ( B @ ( xp @ sdtlseqdt0 ) )
| ( xT @ ( B @ sk22 @ aElementOf0 ) )
| ~ ( xS @ ( B @ aElementOf0 ) ) )
& ( xS @ ( xT @ ( xp @ aUpperBoundOfIn0 ) ) )
& ( ( xp @ ( A @ sdtlseqdt0 ) )
| ~ ( xT @ ( A @ aElementOf0 ) ) )
& ( xf @ ( xp @ aFixedPointOf0 ) )
& ( ( xp @ ( xf @ sdtlpdtrp0 ) )
= xp )
& ( xf @ szDzozmdt0 @ ( xp @ aElementOf0 ) ) ),
inference(cnf,[status(esa)],[232]) ).
thf(237,plain,
xS @ ( xT @ ( xp @ aSupremumOfIn0 ) ),
inference(cnfConj,[status(thm)],[233]) ).
thf(1,conjecture,
? [A: $i] :
( ( xS @ ( xT @ ( A @ aSupremumOfIn0 ) ) )
| ( ! [B: $i] :
( ( ( xS @ ( xT @ ( B @ aUpperBoundOfIn0 ) ) )
& ! [C: $i] :
( ( xT @ ( C @ aElementOf0 ) )
=> ( B @ ( C @ sdtlseqdt0 ) ) )
& ( xS @ ( B @ aElementOf0 ) ) )
=> ( B @ ( A @ sdtlseqdt0 ) ) )
& ( ( xS @ ( xT @ ( A @ aUpperBoundOfIn0 ) ) )
| ( ! [B: $i] :
( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( xS @ ( xT @ ( A @ aSupremumOfIn0 ) ) )
| ( ! [B: $i] :
( ( ( xS @ ( xT @ ( B @ aUpperBoundOfIn0 ) ) )
& ! [C: $i] :
( ( xT @ ( C @ aElementOf0 ) )
=> ( B @ ( C @ sdtlseqdt0 ) ) )
& ( xS @ ( B @ aElementOf0 ) ) )
=> ( B @ ( A @ sdtlseqdt0 ) ) )
& ( ( xS @ ( xT @ ( A @ aUpperBoundOfIn0 ) ) )
| ( ! [B: $i] :
( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(33,plain,
~ ? [A: $i] :
( ( xS @ ( xT @ ( A @ aSupremumOfIn0 ) ) )
| ( ! [B: $i] :
( ( ( xS @ ( xT @ ( B @ aUpperBoundOfIn0 ) ) )
& ! [C: $i] :
( ( xT @ ( C @ aElementOf0 ) )
=> ( B @ ( C @ sdtlseqdt0 ) ) )
& ( xS @ ( B @ aElementOf0 ) ) )
=> ( B @ ( A @ sdtlseqdt0 ) ) )
& ( ( xS @ ( xT @ ( A @ aUpperBoundOfIn0 ) ) )
| ( ! [B: $i] :
( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,plain,
~ ( ? [A: $i] : ( xS @ ( xT @ ( A @ aSupremumOfIn0 ) ) )
| ? [A: $i] :
( ! [B: $i] :
( ( ( xS @ ( xT @ ( B @ aUpperBoundOfIn0 ) ) )
& ! [C: $i] :
( ( xT @ ( C @ aElementOf0 ) )
=> ( B @ ( C @ sdtlseqdt0 ) ) )
& ( xS @ ( B @ aElementOf0 ) ) )
=> ( B @ ( A @ sdtlseqdt0 ) ) )
& ( ( xS @ ( xT @ ( A @ aUpperBoundOfIn0 ) ) )
| ( ! [B: $i] :
( ( xT @ ( B @ aElementOf0 ) )
=> ( A @ ( B @ sdtlseqdt0 ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) )
& ( xS @ ( A @ aElementOf0 ) ) ) ),
inference(miniscope,[status(thm)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( xS @ ( xT @ ( C @ aSupremumOfIn0 ) ) )
& ( ~ ( A @ sk3 @ ( A @ sdtlseqdt0 ) )
| ( A @ sk1 )
| ~ ( xS @ ( A @ aElementOf0 ) ) )
& ( ( xS @ ( xT @ ( A @ sk3 @ aUpperBoundOfIn0 ) ) )
| ( A @ sk1 )
| ~ ( xS @ ( A @ aElementOf0 ) ) )
& ( ( A @ sk3 @ ( B @ sdtlseqdt0 ) )
| ~ ( xT @ ( B @ aElementOf0 ) )
| ( A @ sk1 )
| ~ ( xS @ ( A @ aElementOf0 ) ) )
& ( ( xS @ ( A @ sk3 @ aElementOf0 ) )
| ( A @ sk1 )
| ~ ( xS @ ( A @ aElementOf0 ) ) )
& ( ~ ( A @ sk1 )
| ~ ( xS @ ( xT @ ( A @ aUpperBoundOfIn0 ) ) )
| ~ ( xS @ ( A @ aElementOf0 ) ) )
& ( ~ ( A @ sk1 )
| ~ ( A @ ( A @ sk2 @ sdtlseqdt0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) ) )
& ( ~ ( A @ sk1 )
| ( xT @ ( A @ sk2 @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) )
| ~ ( xS @ ( A @ aElementOf0 ) ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(41,plain,
! [A: $i] :
~ ( xS @ ( xT @ ( A @ aSupremumOfIn0 ) ) ),
inference(cnfConj,[status(thm)],[35]) ).
thf(45,plain,
! [A: $i] :
~ ( xS @ ( xT @ ( A @ aSupremumOfIn0 ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(441,plain,
$false,
inference(rewrite,[status(thm)],[237,45]) ).
thf(442,plain,
$false,
inference(simp,[status(thm)],[441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT388+4 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.13/0.61 % Computer : n002.cluster.edu
% 0.13/0.61 % Model : x86_64 x86_64
% 0.13/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.61 % Memory : 8046.5625MB
% 0.13/0.61 % OS : Linux 6.8.0-71-generic
% 0.13/0.62 % CPULimit : 300
% 0.13/0.62 % WCLimit : 300
% 0.13/0.62 % DateTime : Fri Sep 25 21:42:22 UTC 2026
% 0.13/0.62 % CPUTime :
% 0.13/0.62 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
% 0.99/1.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.45 % [INFO] Parsing done (234ms).
% 1.35/1.46 % [INFO] Running in sequential loop mode.
% 2.21/1.87 % [INFO] eprover registered as external prover.
% 2.21/1.88 % [INFO] Scanning for conjecture ...
% 2.43/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.94 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.96 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.97 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/1.98 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/2.00 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.43/2.01 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.74/2.05 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 2.97/2.14 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.97/2.15 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.17 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.19 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.97/2.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.12/2.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 3.12/2.21 % [INFO] Problem is first-order (TPTP FOF).
% 3.12/2.23 % [INFO] Type checking passed.
% 3.12/2.23 % [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 ...
% 10.32/4.21 % [INFO] Killing All external provers ...
% 10.32/4.22 % Time passed: 3447ms (effective reasoning time: 2743ms)
% 10.32/4.22 % Solved by 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)>
% 10.32/4.22 % Axioms used in derivation (1): m__1330
% 10.32/4.22 % No. of inferences in proof: 13
% 10.32/4.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3447 ms resp. 2743 ms w/o parsing
% 10.32/4.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.32/4.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------