%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM852+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 08:10:11 AM UTC 2026
% Result : Theorem 4.65s 2.85s
% Output : Refutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 294 ( 14 ~; 10 |; 2 &; 248 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 72 !; 6 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vd481_decl,type,
vd481: $i ).
thf(vd469_decl,type,
vd469: $i ).
thf(vd480_decl,type,
vd480: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vskolem9_decl,type,
vskolem9: $i > $i > $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 1)') ).
thf(69,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(61,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(73,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( vd469 @ ( B @ vmul ) @ ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 0)') ).
thf(64,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( vd469 @ ( B @ vmul ) @ ( vd469 @ ( B @ ( A @ vskolem9 ) @ vmul ) @ ( vd469 @ ( B @ vmul ) @ vplus ) @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A
= ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 3)') ).
thf(54,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A
= ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(66,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
| ( B @ ( A @ greater ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ greater ) )
| ( A != B ) ),
file('/export/starexec/sandbox/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)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(31,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(23,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)],[3]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(82,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ greater ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ),
file('/export/starexec/sandbox/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,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( A @ ( B @ less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
vd481 @ ( vd480 @ less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(304), 482, 0)') ).
thf(78,plain,
vd481 @ ( vd480 @ less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
thf(2,negated_conjecture,
~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ( vd469 @ ( vd480 @ vmul ) @ ( vd469 @ ( vd481 @ vmul ) @ greater ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(59,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ less ) )
=> ( A @ ( B @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(76,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ less ) )
| ~ ( B @ ( A @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ vmul ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(303, 0), 0)') ).
thf(39,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
vd480 @ ( vd481 @ greater ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
thf(72,plain,
vd480 @ ( vd481 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 2)') ).
thf(43,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( ( vd469 @ ( A @ vmul ) )
= ( vd469 @ ( B @ ( A @ vskolem9 ) @ ( B @ vplus ) @ vmul ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(200,plain,
$false,
inference(e,[status(thm)],[69,61,73,64,54,66,35,31,23,82,79,46,57,78,22,59,76,39,72,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM852+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n007.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
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 04:11:09 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.82/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/1.19 % [INFO] Parsing done (191ms).
% 1.40/1.20 % [INFO] Running in sequential loop mode.
% 2.04/1.60 % [INFO] eprover registered as external prover.
% 2.04/1.61 % [INFO] Scanning for conjecture ...
% 2.22/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.22/1.76 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.39/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.82 % [INFO] Type checking passed.
% 2.39/1.82 % [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 ...
% 4.65/2.85 % External prover 'e' found a proof!
% 4.65/2.85 % [INFO] Killing All external provers ...
% 4.65/2.85 % Time passed: 2299ms (effective reasoning time: 1639ms)
% 4.65/2.85 % 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)>
% 4.65/2.85 % Axioms used in derivation (19): def(cond(conseq(axiom(3)), 11), 1), holds(antec(304), 482, 0), ass(cond(302, 0), 2), ass(cond(147, 0), 0), ass(cond(281, 0), 0), ass(cond(302, 0), 1), ass(cond(261, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(302, 0), 0), ass(cond(goal(130), 0), 1), ass(cond(302, 0), 3), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), ass(cond(270, 0), 0), holds(conseq_conjunct1(conseq(304)), 483, 0), ass(cond(290, 0), 0), ass(cond(303, 0), 0)
% 4.65/2.85 % No. of inferences in proof: 42
% 4.65/2.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2299 ms resp. 1639 ms w/o parsing
% 5.37/2.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.37/2.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------