%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LAT381+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n006.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 07:47:37 AM UTC 2026
% Result : Theorem 4.24s 2.69s
% Output : Refutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 136 ( 5 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 363 ( 5 ~; 0 |; 39 &; 252 @)
% ( 6 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 64 ( 0 ^; 61 !; 3 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(isEmpty0_decl,type,
isEmpty0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(aLowerBoundOfIn0_decl,type,
aLowerBoundOfIn0: $i > $i > $i > $o ).
thf(sdtlseqdt0_decl,type,
sdtlseqdt0: $i > $i > $o ).
thf(aUpperBoundOfIn0_decl,type,
aUpperBoundOfIn0: $i > $i > $i > $o ).
thf(aInfimumOfIn0_decl,type,
aInfimumOfIn0: $i > $i > $i > $o ).
thf(aSupremumOfIn0_decl,type,
aSupremumOfIn0: $i > $i > $i > $o ).
thf(xu_decl,type,
xu: $i ).
thf(xv_decl,type,
xv: $i ).
thf(aElement0_decl,type,
aElement0: $i > $o ).
thf(xT_decl,type,
xT: $i ).
thf(xS_decl,type,
xS: $i ).
thf(13,axiom,
xT @ ( xS @ aSubsetOf0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725_01) ).
thf(69,plain,
xT @ ( xS @ aSubsetOf0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ aUpperBoundOfIn0 ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ aElementOf0 ) )
=> ( C @ ( D @ sdtlseqdt0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefUB) ).
thf(25,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ aElementOf0 ) )
=> ( C @ ( D @ sdtlseqdt0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) )
=> ( A @ ( B @ ( C @ aUpperBoundOfIn0 ) ) ) )
& ( ( A @ ( B @ ( C @ aUpperBoundOfIn0 ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ aElementOf0 ) )
=> ( C @ ( D @ sdtlseqdt0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
thf(57,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aElementOf0 ) )
=> ( B @ aElement0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ aInfimumOfIn0 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( B @ ( D @ aLowerBoundOfIn0 ) ) )
=> ( C @ ( D @ sdtlseqdt0 ) ) )
& ( A @ ( B @ ( C @ aLowerBoundOfIn0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInf) ).
thf(34,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ ( B @ ( D @ aLowerBoundOfIn0 ) ) )
=> ( C @ ( D @ sdtlseqdt0 ) ) )
& ( A @ ( B @ ( C @ aLowerBoundOfIn0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) )
=> ( A @ ( B @ ( C @ aInfimumOfIn0 ) ) ) )
& ( ( A @ ( B @ ( C @ aInfimumOfIn0 ) ) )
=> ( ! [D: $i] :
( ( A @ ( B @ ( D @ aLowerBoundOfIn0 ) ) )
=> ( C @ ( D @ sdtlseqdt0 ) ) )
& ( A @ ( B @ ( C @ aLowerBoundOfIn0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
( ( xT @ ( xS @ ( xv @ aSupremumOfIn0 ) ) )
& ( xT @ ( xS @ ( xu @ aSupremumOfIn0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__744) ).
thf(80,plain,
( ( xT @ ( xS @ ( xv @ aSupremumOfIn0 ) ) )
& ( xT @ ( xS @ ( xu @ aSupremumOfIn0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
xu = xv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
xu != xv,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
xu != xv,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ aElement0 )
& ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ( ( ( C @ ( B @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( C @ ( A @ sdtlseqdt0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTrans) ).
thf(23,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ aElement0 )
& ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ( ( ( C @ ( B @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( C @ ( A @ sdtlseqdt0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
xT @ aSet0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725) ).
thf(68,plain,
xT @ aSet0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ aSupremumOfIn0 ) ) )
<=> ( ! [D: $i] :
( ( A @ ( B @ ( D @ aUpperBoundOfIn0 ) ) )
=> ( D @ ( C @ sdtlseqdt0 ) ) )
& ( A @ ( B @ ( C @ aUpperBoundOfIn0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSup) ).
thf(70,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( A @ ( B @ ( D @ aUpperBoundOfIn0 ) ) )
=> ( D @ ( C @ sdtlseqdt0 ) ) )
& ( A @ ( B @ ( C @ aUpperBoundOfIn0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) )
=> ( A @ ( B @ ( C @ aSupremumOfIn0 ) ) ) )
& ( ( A @ ( B @ ( C @ aSupremumOfIn0 ) ) )
=> ( ! [D: $i] :
( ( A @ ( B @ ( D @ aUpperBoundOfIn0 ) ) )
=> ( D @ ( C @ sdtlseqdt0 ) ) )
& ( A @ ( B @ ( C @ aUpperBoundOfIn0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ aElement0 )
=> ( A @ ( A @ sdtlseqdt0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mARefl) ).
thf(21,plain,
! [A: $i] :
( ( A @ aElement0 )
=> ( A @ ( A @ sdtlseqdt0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( A @ isEmpty0 )
<=> ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmpty) ).
thf(44,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ( ( ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) )
=> ( A @ isEmpty0 ) )
& ( ( A @ isEmpty0 )
=> ~ ? [B: $i] : ( A @ ( B @ aElementOf0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( A @ ( B @ ( C @ aLowerBoundOfIn0 ) ) )
<=> ( ! [D: $i] :
( ( B @ ( D @ aElementOf0 ) )
=> ( D @ ( C @ sdtlseqdt0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLB) ).
thf(59,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
=> ! [C: $i] :
( ( ( ! [D: $i] :
( ( B @ ( D @ aElementOf0 ) )
=> ( D @ ( C @ sdtlseqdt0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) )
=> ( A @ ( B @ ( C @ aLowerBoundOfIn0 ) ) ) )
& ( ( A @ ( B @ ( C @ aLowerBoundOfIn0 ) ) )
=> ( ! [D: $i] :
( ( B @ ( D @ aElementOf0 ) )
=> ( D @ ( C @ sdtlseqdt0 ) ) )
& ( A @ ( C @ aElementOf0 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( A @ ( B @ aSubsetOf0 ) )
<=> ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
thf(48,plain,
! [A: $i] :
( ( A @ aSet0 )
=> ! [B: $i] :
( ( ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) )
=> ( A @ ( B @ aSubsetOf0 ) ) )
& ( ( A @ ( B @ aSubsetOf0 ) )
=> ( ! [C: $i] :
( ( B @ ( C @ aElementOf0 ) )
=> ( A @ ( C @ aElementOf0 ) ) )
& ( B @ aSet0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ( ( ( A @ ( B @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mASymm) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( B @ aElement0 )
& ( A @ aElement0 ) )
=> ( ( ( A @ ( B @ sdtlseqdt0 ) )
& ( B @ ( A @ sdtlseqdt0 ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(84,plain,
$false,
inference(e,[status(thm)],[69,25,57,34,80,16,23,68,70,21,44,59,48,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT381+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.12/0.40 % Computer : n006.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Fri Sep 25 21:36:56 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.19 % [INFO] Parsing done (209ms).
% 1.42/1.21 % [INFO] Running in sequential loop mode.
% 2.05/1.62 % [INFO] eprover registered as external prover.
% 2.05/1.63 % [INFO] Scanning for conjecture ...
% 2.05/1.68 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.05/1.69 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.70 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.71 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.72 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.23/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 2.41/1.81 % [INFO] Axiom selection finished. Selected 13 axioms (removed 3 axioms).
% 2.41/1.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.83 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.84 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.41/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.41/1.85 % [INFO] Type checking passed.
% 2.41/1.85 % [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 ...
% 4.24/2.69 % External prover 'e' found a proof!
% 4.24/2.69 % [INFO] Killing All external provers ...
% 4.24/2.69 % Time passed: 2143ms (effective reasoning time: 1471ms)
% 4.24/2.69 % 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)>
% 4.24/2.69 % Axioms used in derivation (13): mDefSup, mDefUB, mTrans, mARefl, mDefLB, mDefInf, m__744, mASymm, mDefSub, m__725_01, m__725, mEOfElem, mDefEmpty
% 4.24/2.69 % No. of inferences in proof: 30
% 4.24/2.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2143 ms resp. 1471 ms w/o parsing
% 4.52/2.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.52/2.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------