%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM837+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 : 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 : Sun Sep 27 08:10:07 AM UTC 2026
% Result : Theorem 5.26s 7.40s
% Output : Refutation 5.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 46 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 100 ( 49 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 268 ( 30 ~; 26 |; 6 &; 184 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 101 ( 0 ^; 80 !; 21 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
thf(vd269_decl,type,
vd269: $i ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vd268_decl,type,
vd268: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(v1_decl,type,
v1: $i ).
thf(vd271_decl,type,
vd271: $i ).
thf(11,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(56,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,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(89,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)],[17]) ).
thf(22,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(102,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)],[22]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(33,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
vd271 @ ( vd269 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','(conjunct2(170),272,0)') ).
thf(92,plain,
vd271 @ ( vd269 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(163, 0), 0)') ).
thf(27,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( A @ ( B @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(86,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(31,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ geq ) )
<=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 16), 1)') ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ greater ) ) )
=> ( A @ ( B @ geq ) ) )
& ( ( A @ ( B @ geq ) )
=> ( ( B = A )
| ( A @ ( B @ greater ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(94,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
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(68,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(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ leq ) )
<=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 17), 1)') ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ less ) ) )
=> ( A @ ( B @ leq ) ) )
& ( ( A @ ( B @ leq ) )
=> ( ( B = A )
| ( A @ ( B @ less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
? [A: $i] :
( vd269
= ( A @ ( vd268 @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(171)') ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( vd269
= ( A @ ( vd268 @ vplus ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(24,plain,
~ ? [A: $i] :
( vd269
= ( A @ ( vd268 @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(52,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
=> ( A @ ( B @ less ) ) )
& ( ( A @ ( B @ less ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,axiom,
vd269 @ ( vd268 @ less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
thf(93,plain,
vd269 @ ( vd268 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(158, 0), 0)') ).
thf(29,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,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(76,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,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(39,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(98,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(80,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(35,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(126,plain,
$false,
inference(e,[status(thm)],[56,89,102,33,92,27,86,31,58,94,68,42,24,52,110,93,29,76,39,98,80,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM837+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
% 0.21/5.47 % Computer : n020.cluster.edu
% 0.21/5.47 % Model : x86_64 x86_64
% 0.21/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/5.47 % Memory : 8046.5625MB
% 0.21/5.47 % OS : Linux 6.8.0-71-generic
% 0.21/5.48 % CPULimit : 300
% 0.21/5.48 % WCLimit : 300
% 0.21/5.48 % DateTime : Sat Sep 26 04:12:24 UTC 2026
% 0.21/5.48 % CPUTime :
% 0.21/5.48 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
% 0.26/5.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.55/6.14 % [INFO] Parsing done (174ms).
% 1.55/6.16 % [INFO] Running in sequential loop mode.
% 2.31/6.49 % [INFO] eprover registered as external prover.
% 2.31/6.49 % [INFO] Scanning for conjecture ...
% 2.44/6.57 % [INFO] Found a conjecture (or negated_conjecture) and 21 axioms. Running axiom selection ...
% 2.70/6.62 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 2.70/6.66 % [INFO] Problem is first-order (TPTP FOF).
% 2.70/6.67 % [INFO] Type checking passed.
% 2.70/6.67 % [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 ...
% 4.79/7.39 % External prover 'e' found a proof!
% 4.79/7.40 % [INFO] Killing All external provers ...
% 4.79/7.40 % Time passed: 1788ms (effective reasoning time: 1235ms)
% 4.79/7.40 % 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)>
% 5.26/7.40 % Axioms used in derivation (21): def(cond(conseq(axiom(3)), 11), 1), def(cond(conseq(axiom(3)), 16), 1), ass(cond(goal(88), 0), 2), ass(cond(goal(130), 0), 2), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(81, 0), 0), ass(cond(goal(130), 0), 1), ass(cond(163, 0), 0), (conjunct2(170),272,0), ass(cond(goal(88), 0), 1), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), holds(conjunct1(170), 270, 0), ass(cond(goal(88), 0), 3), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(147, 0), 0), ass(cond(goal(88), 0), 0), def(cond(conseq(axiom(3)), 17), 1), ass(cond(158, 0), 0), ass(cond(33, 0), 0)
% 5.26/7.40 % No. of inferences in proof: 46
% 5.26/7.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1788 ms resp. 1235 ms w/o parsing
% 5.50/7.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.50/7.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------