%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM841+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 08:10:08 AM UTC 2026
% Result : Theorem 6.05s 3.79s
% Output : Refutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 26
% Syntax : Number of formulae : 54 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 86 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 310 ( 12 ~; 8 |; 3 &; 266 @)
% ( 1 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 91 ( 0 ^; 86 !; 5 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vd344_decl,type,
vd344: $i ).
thf(vd347_decl,type,
vd347: $i ).
thf(vd345_decl,type,
vd345: $i ).
thf(vd348_decl,type,
vd348: $i ).
thf(v1_decl,type,
v1: $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(vskolem2_decl,type,
vskolem2: $i > $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(16,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(69,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)],[16]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(74,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,conjecture,
vd348 @ ( vd345 @ vplus ) @ ( vd347 @ ( vd344 @ vplus ) @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(214, 352, 0)') ).
thf(2,negated_conjecture,
~ ( vd348 @ ( vd345 @ vplus ) @ ( vd347 @ ( vd344 @ vplus ) @ greater ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(28,plain,
~ ( vd348 @ ( vd345 @ vplus ) @ ( vd347 @ ( vd344 @ vplus ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
vd347 @ ( vd345 @ vplus ) @ ( vd347 @ ( vd344 @ vplus ) @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(212, 350, 0)') ).
thf(65,plain,
vd347 @ ( vd345 @ vplus ) @ ( vd347 @ ( vd344 @ vplus ) @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
vd345 @ ( vd348 @ vplus ) @ ( vd345 @ ( vd347 @ vplus ) @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 1)') ).
thf(44,plain,
vd345 @ ( vd348 @ vplus ) @ ( vd345 @ ( vd347 @ vplus ) @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 2)') ).
thf(54,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) )
=> ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( A = B )
=> ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
thf(72,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ vplus ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(40,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(58,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(94,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 0)') ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) )
=> ( B @ ( A @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ greater ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(46,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
=> ( A @ ( B @ greater ) ) )
& ( ( A @ ( B @ greater ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
vd348 @ ( vd347 @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct2(211), 349, 0)') ).
thf(57,plain,
vd348 @ ( vd347 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(29,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(60,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(202), 0), 1)') ).
thf(85,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ vplus ) )
= ( C @ ( B @ vplus ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
( ( vd347 @ ( vd345 @ vplus ) )
= ( vd345 @ ( vd347 @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 0)') ).
thf(102,plain,
( ( vd347 @ ( vd345 @ vplus ) )
= ( vd345 @ ( vd347 @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ greater ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).
thf(77,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ greater ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,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(96,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,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(32,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)],[4]) ).
thf(7,axiom,
vd345 @ ( vd344 @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(211), 346, 0)') ).
thf(45,plain,
vd345 @ ( vd344 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ less ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).
thf(91,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ less ) )
=> ( C @ ( B @ vplus ) @ ( C @ ( A @ vplus ) @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(66,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(99,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
( ( vd345 @ ( vd348 @ vplus ) )
= ( vd348 @ ( vd345 @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(213, 351, 2)') ).
thf(104,plain,
( ( vd345 @ ( vd348 @ vplus ) )
= ( vd348 @ ( vd345 @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(155,plain,
$false,
inference(e,[status(thm)],[69,74,28,65,44,54,80,72,40,58,94,62,46,57,29,60,85,102,77,96,32,45,91,66,99,104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM841+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.11 % 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
% 0.23/0.49 % Computer : n009.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Sat Sep 26 04:12:29 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.38/1.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.89/1.61 % [INFO] Parsing done (277ms).
% 1.89/1.64 % [INFO] Running in sequential loop mode.
% 2.89/2.24 % [INFO] eprover registered as external prover.
% 2.89/2.25 % [INFO] Scanning for conjecture ...
% 3.05/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 25 axioms. Running axiom selection ...
% 3.24/2.47 % [INFO] Axiom selection finished. Selected 25 axioms (removed 0 axioms).
% 3.42/2.55 % [INFO] Problem is first-order (TPTP FOF).
% 3.42/2.56 % [INFO] Type checking passed.
% 3.42/2.57 % [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 ...
% 6.05/3.78 % External prover 'e' found a proof!
% 6.05/3.78 % [INFO] Killing All external provers ...
% 6.05/3.78 % Time passed: 3078ms (effective reasoning time: 2138ms)
% 6.05/3.78 % 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)>
% 6.05/3.79 % Axioms used in derivation (25): ass(cond(goal(193), 0), 0), ass(cond(goal(193), 0), 2), def(cond(conseq(axiom(3)), 11), 1), holds(213, 351, 0), ass(cond(goal(130), 0), 0), ass(cond(goal(88), 0), 3), ass(cond(goal(202), 0), 2), ass(cond(goal(202), 0), 1), ass(cond(52, 0), 0), ass(cond(61, 0), 0), holds(conjunct1(211), 346, 0), ass(cond(140, 0), 0), ass(cond(goal(193), 0), 1), ass(cond(189, 0), 0), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(147, 0), 0), ass(cond(20, 0), 0), holds(213, 351, 1), ass(cond(33, 0), 0), holds(213, 351, 2), ass(cond(goal(130), 0), 2), ass(cond(goal(202), 0), 0), holds(conjunct2(211), 349, 0), ass(cond(43, 0), 0), holds(212, 350, 0)
% 6.05/3.79 % No. of inferences in proof: 54
% 6.05/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3078 ms resp. 2138 ms w/o parsing
% 6.67/3.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.67/3.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------