%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV604^1 : TPTP v9.3.1. Released v9.3.0.
% 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 : Wed Sep 30 08:37:25 AM UTC 2026
% Result : Theorem 3.64s 2.20s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 12 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 99 ( 4 ~; 2 |; 0 &; 93 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(bot_decl,type,
bot:
!>[TA: $tType] : TA ).
thf(insert_decl,type,
insert:
!>[TA: $tType] : ( TA > ( set @ TA ) > ( set @ TA ) ) ).
thf(vimage_decl,type,
vimage:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( set @ TA ) > ( set @ TB ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a2_decl,type,
a2: a ).
thf(b2_decl,type,
b2: b ).
thf(f_decl,type,
f: a > b ).
thf(1,conjecture,
( ( member @ a @ a2 @ ( vimage @ a @ b @ f @ ( insert @ b @ b2 @ ( bot @ ( set @ b ) ) ) ) )
= ( ( f @ a2 )
= b2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vimage_singleton_eq) ).
thf(2,negated_conjecture,
( ( member @ a @ a2 @ ( vimage @ a @ b @ f @ ( insert @ b @ b2 @ ( bot @ ( set @ b ) ) ) ) )
!= ( ( f @ a2 )
= b2 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
( ( member @ a @ a2 @ ( vimage @ a @ b @ f @ ( insert @ b @ b2 @ ( bot @ ( set @ b ) ) ) ) )
!= ( ( f @ a2 )
= b2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
= ( member @ TA @ ( B @ A ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vimage_eq) ).
thf(8,plain,
! [TA: $tType,TB: $tType,A: TB,B: TB > TA,C: set @ TA] :
( ( member @ TB @ A @ ( vimage @ TB @ TA @ B @ C ) )
= ( member @ TA @ ( B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot @ ( set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_iff) ).
thf(11,plain,
! [TA: $tType,A: TA] :
~ ( member @ TA @ A @ ( bot @ ( set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insert_iff) ).
thf(13,plain,
! [TA: $tType,A: TA,B: TA,C: set @ TA] :
( ( member @ TA @ A @ ( insert @ TA @ B @ C ) )
= ( ( A = B )
| ( member @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(20,plain,
$false,
inference(e,[status(thm)],[6,8,11,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV604^1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.10/0.22 % Computer : n002.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 16:02:22 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.02/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.99 % [INFO] Parsing done (186ms).
% 1.20/1.00 % [INFO] Running in sequential loop mode.
% 1.79/1.40 % [INFO] eprover registered as external prover.
% 1.98/1.40 % [INFO] Scanning for conjecture ...
% 2.13/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.13/1.54 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.13/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.13/1.57 % [INFO] Type checking passed.
% 2.13/1.57 % [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 ...
% 3.50/2.20 % External prover 'e' found a proof!
% 3.50/2.20 % [INFO] Killing All external provers ...
% 3.64/2.20 % Time passed: 1830ms (effective reasoning time: 1186ms)
% 3.64/2.20 % 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)>
% 3.64/2.20 % Axioms used in derivation (3): vimage_eq, empty_iff, insert_iff
% 3.64/2.20 % No. of inferences in proof: 10
% 3.64/2.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1830 ms resp. 1186 ms w/o parsing
% 3.64/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.64/2.24 % [INFO] Killing All external provers ...
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