%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% 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 : n013.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 08:14:20 AM UTC 2026
% Result : Theorem 3.86s 2.16s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 16 ( 11 unt; 0 typ; 6 def)
% Number of atoms : 62 ( 6 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 106 ( 2 ~; 2 |; 4 &; 86 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 41 ( 17 ^; 20 !; 4 ?; 41 :)
% 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(mor_decl,type,
mor: ( 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(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(big_q_decl,type,
big_q: $i > mworld > $o ).
thf(big_p_decl,type,
big_p: $i > mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mor_def,definition,
( mor
= ( ^ [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(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(1,conjecture,
( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_p @ A ) ) @ ( mor @ ( mbox @ ( big_q @ A ) ) @ ( mbox @ ( big_p @ B ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2137) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mexists_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( big_p @ A ) ) @ ( mor @ ( mbox @ ( big_q @ A ) ) @ ( mbox @ ( big_p @ B ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ? [A: $i] :
( ( eiw_di @ A @ mactual )
& ! [B: mworld] :
( ( mrel @ mactual @ B )
=> ! [C: $i] :
( ( eiw_di @ C @ B )
=> ! [D: mworld] :
( ( mrel @ B @ D )
=> ( ! [E: mworld] :
( ( mrel @ D @ E )
=> ( big_p @ A @ E ) )
=> ( ! [E: mworld] :
( ( mrel @ D @ E )
=> ( big_q @ A @ E ) )
| ! [E: mworld] :
( ( mrel @ D @ E )
=> ( big_p @ C @ E ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).
thf(16,plain,
! [A: mworld,B: mworld] : ( mrel @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(18,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ A @ B ) )
=> ( eiw_di @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_cumul) ).
thf(20,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)],[5]) ).
thf(22,plain,
$false,
inference(e,[status(thm)],[6,16,18,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL958^18 : TPTP v9.3.1. Released v8.1.0.
% 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
% 0.09/0.21 % Computer : n013.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 10:54:36 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 0.84/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.99 % [INFO] Parsing done (205ms).
% 1.16/1.00 % [INFO] Running in sequential loop mode.
% 2.12/1.41 % [INFO] eprover registered as external prover.
% 2.12/1.41 % [INFO] Scanning for conjecture ...
% 2.32/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.32/1.58 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.32/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.32/1.59 % [INFO] Type checking passed.
% 2.32/1.60 % [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 ...
% 3.86/2.16 % External prover 'e' found a proof!
% 3.86/2.16 % [INFO] Killing All external provers ...
% 3.86/2.16 % Time passed: 1807ms (effective reasoning time: 1148ms)
% 3.86/2.16 % 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)>
% 3.86/2.16 % Axioms used in derivation (3): mrel_universal, eiw_di_nonempty, eiw_di_cumul
% 3.86/2.16 % No. of inferences in proof: 10
% 3.86/2.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1807 ms resp. 1148 ms w/o parsing
% 4.03/2.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.03/2.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------