%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 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 : n017.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 : Sun Sep 27 08:10:09 AM UTC 2026
% Result : Theorem 6.54s 3.63s
% Output : Refutation 6.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 54 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 480 ( 2 ~; 0 |; 4 &; 455 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 ^; 39 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(vd411_decl,type,
vd411: $i ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(v1_decl,type,
v1: $i ).
thf(14,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(60,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( vd411 @ vsucc @ ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) )
= ( vd411 @ vsucc @ ( A @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 5)') ).
thf(38,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( vd411 @ vsucc @ ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) )
= ( vd411 @ vsucc @ ( A @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( vd411 @ vsucc @ ( A @ ( vd411 @ vsucc @ vmul ) @ vplus ) )
= ( vd411 @ vsucc @ ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 6)') ).
thf(41,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( vd411 @ vsucc @ ( A @ ( vd411 @ vsucc @ vmul ) @ vplus ) )
= ( vd411 @ vsucc @ ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ vsucc @ vmul ) )
= ( vd411 @ vsucc @ ( A @ ( vd411 @ vsucc @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 7)') ).
thf(44,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ vsucc @ vmul ) )
= ( vd411 @ vsucc @ ( A @ ( vd411 @ vsucc @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(49,plain,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( vd411 @ vsucc @ ( A @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ ( vd411 @ vsucc @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 4)') ).
thf(35,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( vd411 @ vsucc @ ( A @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ ( vd411 @ vsucc @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(63,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
( ( v1 @ ( vd411 @ vmul ) @ vsucc )
= ( v1 @ ( v1 @ ( vd411 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 2)') ).
thf(47,plain,
( ( v1 @ ( vd411 @ vmul ) @ vsucc )
= ( v1 @ ( v1 @ ( vd411 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(57,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ ( vd411 @ vplus ) @ vsucc @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ vsucc @ ( vd411 @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 2)') ).
thf(29,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ ( vd411 @ vplus ) @ vsucc @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ vsucc @ ( vd411 @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ ( vd411 @ vsucc @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ ( vd411 @ vplus ) @ vsucc @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 3)') ).
thf(32,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ ( vd411 @ vsucc @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ ( vd411 @ vplus ) @ vsucc @ ( A @ ( vd411 @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ vsucc @ vmul ) )
= ( A @ vsucc @ ( A @ vsucc @ ( vd411 @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ vsucc @ vmul ) )
= ( A @ vsucc @ ( A @ vsucc @ ( vd411 @ vmul ) @ vplus ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ vsucc @ vmul ) )
= ( A @ vsucc @ ( A @ vsucc @ ( vd411 @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ vsucc @ ( vd411 @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 1)') ).
thf(26,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ vplus ) @ ( A @ ( vd411 @ vmul ) @ vplus ) )
= ( A @ vsucc @ ( vd411 @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) )
= ( A @ vsucc @ ( A @ vsucc @ ( vd411 @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 0)') ).
thf(23,plain,
! [A: $i] :
( ( ( A @ ( vd411 @ vsucc @ vmul ) )
= ( A @ ( A @ ( vd411 @ vmul ) @ vplus ) ) )
=> ( ( A @ vsucc @ ( vd411 @ ( A @ ( vd411 @ vmul ) @ vplus ) @ vplus ) )
= ( A @ vsucc @ ( A @ vsucc @ ( vd411 @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(77,plain,
$false,
inference(e,[status(thm)],[60,38,41,44,49,66,35,63,47,57,29,32,17,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.14/0.40 % Computer : n017.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 04:08:04 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.30/1.22 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.86/1.53 % [INFO] Parsing done (309ms).
% 1.86/1.55 % [INFO] Running in sequential loop mode.
% 3.10/2.18 % [INFO] eprover registered as external prover.
% 3.10/2.20 % [INFO] Scanning for conjecture ...
% 3.42/2.35 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 3.58/2.41 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 3.58/2.48 % [INFO] Problem is first-order (TPTP FOF).
% 3.58/2.49 % [INFO] Type checking passed.
% 3.83/2.50 % [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 ...
% 6.54/3.63 % External prover 'e' found a proof!
% 6.54/3.63 % [INFO] Killing All external provers ...
% 6.54/3.63 % Time passed: 3031ms (effective reasoning time: 2067ms)
% 6.54/3.63 % 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)>
% 6.54/3.63 % Axioms used in derivation (14): ass(cond(conseq(263), 1), 4), ass(cond(conseq(263), 1), 7), ass(cond(conseq(263), 1), 6), ass(cond(conseq(263), 1), 1), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(61, 0), 0), holds(264, 412, 2), ass(cond(conseq(263), 1), 3), ass(cond(43, 0), 0), ass(cond(conseq(263), 1), 5), ass(cond(conseq(263), 1), 0), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), ass(cond(conseq(263), 1), 2), ass(cond(33, 0), 0)
% 6.54/3.63 % No. of inferences in proof: 32
% 6.54/3.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3031 ms resp. 2067 ms w/o parsing
% 6.80/3.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.80/3.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------