%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PRO029^16 : 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 : n020.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 08:20:29 AM UTC 2026
% Result : Theorem 4.12s 2.23s
% Output : Refutation 4.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 16
% Syntax : Number of formulae : 29 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 136 ( 5 equ; 0 cnn)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 245 ( 11 ~; 0 |; 8 &; 198 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 42 ( 12 ^; 30 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mindex_type,type,
mindex: $tType ).
thf(mrel_decl,type,
mrel: mindex > mworld > mworld > $o ).
thf('#c_decl',type,
'#c': mindex ).
thf('#u_decl',type,
'#u': mindex ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $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: mindex > ( mworld > $o ) > mworld > $o ).
thf(charge_decl,type,
charge: mworld > $o ).
thf(called_decl,type,
called: mworld > $o ).
thf(paid_decl,type,
paid: mworld > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
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: mindex,B: mworld > $o,C: mworld] :
! [D: mworld] :
( ( mrel @ A @ C @ D )
=> ( B @ D ) ) ) ) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ '#c' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#c_reflexive') ).
thf(20,plain,
! [A: mworld] : ( mrel @ '#c' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
mlocal @ ( mimplies @ paid @ called ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aciom_paid_charge) ).
thf(28,plain,
( ( paid @ mactual )
=> ( called @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',requirement_1) ).
thf(2,negated_conjecture,
~ ( mlocal @ ( mimplies @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) @ ( mbox @ '#u' @ ( mnot @ ( mimplies @ charge @ ( mand @ called @ ( mnot @ paid ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ( ~ ( ( charge @ mactual )
=> ( ( called @ mactual )
& ~ ( paid @ mactual ) ) )
=> ! [A: mworld] :
( ( mrel @ '#u' @ mactual @ A )
=> ~ ( ( charge @ A )
=> ( ( called @ A )
& ~ ( paid @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#c' @ A @ B )
& ( mrel @ '#c' @ B @ C ) )
=> ( mrel @ '#c' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#c_transitive') ).
thf(22,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#c' @ A @ B )
& ( mrel @ '#c' @ B @ C ) )
=> ( mrel @ '#c' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#c' @ called ) ) @ ( mbox @ '#u' @ ( mnot @ ( mbox @ '#c' @ called ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(39,plain,
( ~ ! [A: mworld] :
( ( mrel @ '#c' @ mactual @ A )
=> ( called @ A ) )
=> ! [A: mworld] :
( ( mrel @ '#u' @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ '#c' @ A @ B )
=> ( called @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
mlocal @ ( mbox @ '#u' @ ( mimplies @ called @ ( mbox @ '#c' @ called ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(35,plain,
! [A: mworld] :
( ( mrel @ '#u' @ mactual @ A )
=> ( ( called @ A )
=> ! [B: mworld] :
( ( mrel @ '#c' @ A @ B )
=> ( called @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
mlocal @ ( mimplies @ ( mnot @ ( mbox @ '#u' @ paid ) ) @ ( mbox @ '#c' @ ( mnot @ ( mbox @ '#u' @ paid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(43,plain,
( ~ ! [A: mworld] :
( ( mrel @ '#u' @ mactual @ A )
=> ( paid @ A ) )
=> ! [A: mworld] :
( ( mrel @ '#c' @ mactual @ A )
=> ~ ! [B: mworld] :
( ( mrel @ '#u' @ A @ B )
=> ( paid @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#u' @ A @ B )
& ( mrel @ '#u' @ B @ C ) )
=> ( mrel @ '#u' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#u_transitive') ).
thf(26,plain,
! [A: mworld,B: mworld,C: mworld] :
( ( ( mrel @ '#u' @ A @ B )
& ( mrel @ '#u' @ B @ C ) )
=> ( mrel @ '#u' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
mlocal @ ( mimplies @ charge @ ( mand @ ( mbox @ '#u' @ charge ) @ ( mbox @ '#c' @ charge ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_charge_u) ).
thf(30,plain,
( ( charge @ mactual )
=> ( ! [A: mworld] :
( ( mrel @ '#u' @ mactual @ A )
=> ( charge @ A ) )
& ! [A: mworld] :
( ( mrel @ '#c' @ mactual @ A )
=> ( charge @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: mworld] : ( mrel @ '#u' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#u_reflexive') ).
thf(24,plain,
! [A: mworld] : ( mrel @ '#u' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
mlocal @ ( mbox @ '#c' @ ( mimplies @ paid @ ( mbox @ '#u' @ paid ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(37,plain,
! [A: mworld] :
( ( mrel @ '#c' @ mactual @ A )
=> ( ( paid @ A )
=> ! [B: mworld] :
( ( mrel @ '#u' @ A @ B )
=> ( paid @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(47,plain,
$false,
inference(e,[status(thm)],[20,28,13,22,39,35,43,26,30,24,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PRO029^16 : 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
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:22:19 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.00 % [INFO] Parsing done (226ms).
% 1.23/1.01 % [INFO] Running in sequential loop mode.
% 2.21/1.41 % [INFO] eprover registered as external prover.
% 2.21/1.42 % [INFO] Scanning for conjecture ...
% 2.41/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.41/1.58 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.60/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.60/1.61 % [INFO] Type checking passed.
% 2.60/1.61 % [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 ...
% 4.12/2.22 % External prover 'e' found a proof!
% 4.12/2.23 % [INFO] Killing All external provers ...
% 4.12/2.23 % Time passed: 1900ms (effective reasoning time: 1208ms)
% 4.12/2.23 % 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)>
% 4.12/2.23 % Axioms used in derivation (10): mrel_#c_reflexive, axiom_2, mrel_#u_reflexive, axiom_charge_u, axiom_3, axiom_1, aciom_paid_charge, mrel_#u_transitive, mrel_#c_transitive, axiom_4
% 4.12/2.23 % No. of inferences in proof: 24
% 4.12/2.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1900 ms resp. 1208 ms w/o parsing
% 4.12/2.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.12/2.29 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------