%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO891^16 : TPTP v9.3.1. Released v8.1.0.
% 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 : n011.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 08:46:12 AM UTC 2026
% Result : Theorem 4.18s 2.34s
% Output : Refutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 7 def)
% Number of atoms : 114 ( 7 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 217 ( 2 ~; 0 |; 14 &; 179 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-3 aty)
% Number of variables : 64 ( 27 ^; 28 !; 9 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mand_decl,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mbox_decl,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mdia_decl,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(eiw_di_decl,type,
eiw_di: $i > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_decl,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(p_decl,type,
p: $i > mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: mworld > $o,B: mworld] :
! [C: mworld] :
( ( mrel @ B @ C )
=> ( A @ C ) ) ) ) ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: mworld > $o,B: mworld] :
? [C: mworld] :
( ( mrel @ B @ C )
& ( A @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] :
( ( eiw_di @ C @ B )
& ( A @ C @ B ) ) ) ) ).
thf(5,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(24,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(20,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(28,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ A @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_transitive) ).
thf(22,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ A @ B )
& ( mrel @ B @ C ) )
=> ( mrel @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( mexists_di @ ( qmltpeq @ A ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] : ( mdia @ ( p @ A ) ) )
@ ( mdia @ ( mexists_di @ p ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mforall_di
@ ^ [A: $i] : ( mbox @ ( mexists_di @ ( qmltpeq @ A ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [A: $i] : ( mdia @ ( p @ A ) ) )
@ ( mdia @ ( mexists_di @ p ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ( ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ? [C: $i] :
( ( eiw_di @ C @ B )
& ( qmltpeq @ A @ C @ B ) ) ) )
=> ( ? [A: $i] :
( ( eiw_di @ A @ mactual )
& ? [B: mworld] :
( ( mrel @ mactual @ B )
& ( p @ A @ B ) ) )
=> ? [A: mworld] :
( ( mrel @ mactual @ A )
& ? [B: $i] :
( ( eiw_di @ B @ A )
& ( p @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ A @ B ) )
=> ( eiw_di @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(26,plain,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ A @ B ) )
=> ( eiw_di @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(30,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ B @ A @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ C ) ) @ ( qmltpeq @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(32,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( qmltpeq @ B @ C @ mactual ) )
=> ( qmltpeq @ A @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( p @ A ) ) @ ( p @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p_substitution_1) ).
thf(34,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( p @ A @ mactual ) )
=> ( p @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[24,20,28,22,11,26,30,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO891^16 : TPTP v9.3.1. Released v8.1.0.
% 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 : n011.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 17:26:01 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
% 1.01/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.04 % [INFO] Parsing done (220ms).
% 1.43/1.05 % [INFO] Running in sequential loop mode.
% 2.10/1.48 % [INFO] eprover registered as external prover.
% 2.10/1.49 % [INFO] Scanning for conjecture ...
% 2.53/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.53/1.66 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.53/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.53/1.68 % [INFO] Type checking passed.
% 2.53/1.69 % [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 ...
% 4.18/2.33 % External prover 'e' found a proof!
% 4.18/2.33 % [INFO] Killing All external provers ...
% 4.18/2.33 % Time passed: 1969ms (effective reasoning time: 1273ms)
% 4.18/2.33 % 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)>
% 4.18/2.34 % Axioms used in derivation (8): p_substitution_1, mrel_reflexive, eiw_di_cumul, reflexivity, eiw_di_nonempty, mrel_transitive, transitivity, symmetry
% 4.18/2.34 % No. of inferences in proof: 20
% 4.18/2.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1969 ms resp. 1273 ms w/o parsing
% 4.44/2.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.44/2.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------