%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP012^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : n009.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 08:06:20 AM UTC 2026
% Result : Theorem 4.15s 2.22s
% Output : Refutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 11 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 79 ( 2 ~; 0 |; 2 &; 70 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(u_type,type,
u: $tType ).
thf(d_type,type,
d: $tType ).
thf(du_type,type,
du: $tType ).
thf(mono_2Etyop_2Einteger_2Eint_type,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(mono_2Ec_2Einteger_2Eint__add_decl,type,
mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__divides_decl,type,
mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__neg_decl,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__sub_decl,type,
mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(1,conjecture,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RSUB) ).
thf(2,negated_conjecture,
~ ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__sub @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2Eint__sub) ).
thf(12,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ A @ B )
= ( mono_2Ec_2Einteger_2Eint__add @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__RADD) ).
thf(15,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint,C: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ A @ B )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__add @ C @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__DIVIDES__NEG) ).
thf(19,plain,
! [A: mono_2Etyop_2Einteger_2Eint,B: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ A @ ( mono_2Ec_2Einteger_2Eint__neg @ B ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ A ) @ B )
= ( mono_2Ec_2Einteger_2Eint__divides @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
$false,
inference(e,[status(thm)],[6,12,15,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP012^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.09/0.21 % Computer : n009.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 19:27:00 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.83/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.07 % [INFO] Parsing done (298ms).
% 1.60/1.09 % [INFO] Running in sequential loop mode.
% 2.37/1.46 % [INFO] eprover registered as external prover.
% 2.37/1.47 % [INFO] Scanning for conjecture ...
% 2.75/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 67 axioms. Running axiom selection ...
% 2.75/1.65 % [INFO] Axiom selection finished. Selected 3 axioms (removed 64 axioms).
% 2.75/1.66 % [INFO] Problem is higher-order (TPTP THF).
% 2.75/1.67 % [INFO] Type checking passed.
% 2.75/1.67 % [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 ...
% 4.15/2.22 % External prover 'e' found a proof!
% 4.15/2.22 % [INFO] Killing All external provers ...
% 4.15/2.22 % Time passed: 1878ms (effective reasoning time: 1124ms)
% 4.15/2.22 % 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)>
% 4.15/2.22 % Axioms used in derivation (3): thm_2Einteger_2Eint__sub, thm_2Einteger_2EINT__DIVIDES__RADD, thm_2Einteger_2EINT__DIVIDES__NEG
% 4.15/2.22 % No. of inferences in proof: 10
% 4.15/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1878 ms resp. 1124 ms w/o parsing
% 4.15/2.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.15/2.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------