%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM844+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 : 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 : Sun Sep 27 08:10:09 AM UTC 2026
% Result : Theorem 5.45s 3.31s
% Output : Refutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 45 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 298 ( 10 ~; 0 |; 4 &; 276 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vd411_decl,type,
vd411: $i ).
thf(vd413_decl,type,
vd413: $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(v1_decl,type,
v1: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(vskolem2_decl,type,
vskolem2: $i > $i ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(24,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,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(33,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)],[7]) ).
thf(12,axiom,
( ( v1 @ ( vd411 @ vmul ) @ vsucc )
= ( v1 @ ( v1 @ ( vd411 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 2)') ).
thf(53,plain,
( ( v1 @ ( vd411 @ vmul ) @ vsucc )
= ( v1 @ ( v1 @ ( vd411 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(41,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ vsucc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(71,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(15,axiom,
( ( vd413 @ ( vd411 @ vsucc @ vmul ) )
= ( vd413 @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(265, 414, 0)') ).
thf(66,plain,
( ( vd413 @ ( vd411 @ vsucc @ vmul ) )
= ( vd413 @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
( ( vd411 @ vsucc )
= ( v1 @ ( vd411 @ vmul ) @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 1)') ).
thf(80,plain,
( ( vd411 @ vsucc )
= ( v1 @ ( vd411 @ vmul ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
( ( v1 @ ( vd411 @ vsucc @ vmul ) )
= ( vd411 @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(264, 412, 0)') ).
thf(31,plain,
( ( v1 @ ( vd411 @ vsucc @ vmul ) )
= ( vd411 @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(43,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,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(55,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)],[13]) ).
thf(11,axiom,
( ( vd413 @ vsucc @ ( vd411 @ vsucc @ vmul ) )
= ( vd411 @ vsucc @ ( vd413 @ ( vd411 @ vsucc @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 0)') ).
thf(51,plain,
( ( vd413 @ vsucc @ ( vd411 @ vsucc @ vmul ) )
= ( vd411 @ vsucc @ ( vd413 @ ( vd411 @ vsucc @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(68,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(19,axiom,
( ( vd411 @ vsucc @ ( vd413 @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) @ vplus ) )
= ( vd411 @ vsucc @ ( vd413 @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 2)') ).
thf(78,plain,
( ( vd411 @ vsucc @ ( vd413 @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) @ vplus ) )
= ( vd411 @ vsucc @ ( vd413 @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
( ( vd411 @ vsucc @ ( vd413 @ ( vd411 @ vsucc @ vmul ) @ vplus ) )
= ( vd411 @ vsucc @ ( vd413 @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 1)') ).
thf(29,plain,
( ( vd411 @ vsucc @ ( vd413 @ ( vd411 @ vsucc @ vmul ) @ vplus ) )
= ( vd411 @ vsucc @ ( vd413 @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( ( vd411 @ vsucc @ ( vd413 @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) )
= ( vd413 @ ( vd411 @ vsucc @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(266, 415, 3)') ).
thf(2,negated_conjecture,
( ( vd411 @ vsucc @ ( vd413 @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) )
!= ( vd413 @ ( vd411 @ vsucc @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
( ( vd411 @ vsucc @ ( vd413 @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) )
!= ( vd413 @ ( vd411 @ vsucc @ vplus ) @ ( vd413 @ ( vd411 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(27,plain,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(48,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(14,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)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(75,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(82,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(90,plain,
$false,
inference(e,[status(thm)],[24,33,53,41,71,66,80,31,43,55,51,68,78,29,22,27,48,63,75,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM844+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.10 % 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
% 0.21/0.45 % Computer : n009.cluster.edu
% 0.21/0.45 % Model : x86_64 x86_64
% 0.21/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.45 % Memory : 8046.5625MB
% 0.21/0.45 % OS : Linux 6.8.0-71-generic
% 0.21/0.45 % CPULimit : 300
% 0.21/0.45 % WCLimit : 300
% 0.21/0.45 % DateTime : Sat Sep 26 04:12:44 UTC 2026
% 0.21/0.45 % CPUTime :
% 0.21/0.45 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
% 1.26/1.23 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.63/1.42 % [INFO] Parsing done (190ms).
% 1.63/1.44 % [INFO] Running in sequential loop mode.
% 2.48/2.00 % [INFO] eprover registered as external prover.
% 2.48/2.01 % [INFO] Scanning for conjecture ...
% 2.78/2.15 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 3.05/2.24 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 3.26/2.31 % [INFO] Problem is first-order (TPTP FOF).
% 3.26/2.31 % [INFO] Type checking passed.
% 3.26/2.32 % [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 ...
% 5.45/3.30 % External prover 'e' found a proof!
% 5.45/3.30 % [INFO] Killing All external provers ...
% 5.45/3.30 % Time passed: 2644ms (effective reasoning time: 1859ms)
% 5.45/3.30 % 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)>
% 5.45/3.31 % Axioms used in derivation (19): ass(cond(6, 0), 0), holds(266, 415, 2), holds(265, 414, 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), holds(266, 415, 0), ass(cond(253, 0), 0), ass(cond(52, 0), 0), ass(cond(61, 0), 0), ass(cond(241, 0), 0), ass(cond(12, 0), 0), ass(cond(43, 0), 0), holds(266, 415, 1), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), holds(264, 412, 1), ass(cond(20, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0), holds(264, 412, 2), holds(264, 412, 0)
% 5.45/3.31 % No. of inferences in proof: 42
% 5.45/3.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2644 ms resp. 1859 ms w/o parsing
% 5.45/3.39 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.45/3.39 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------