%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM851+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 : n001.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 4.83s 2.70s
% Output : Refutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 84 ( 70 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 328 ( 28 ~; 10 |; 5 &; 272 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 107 ( 0 ^; 92 !; 15 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vd471_decl,type,
vd471: $i ).
thf(vd473_decl,type,
vd473: $i ).
thf(vd469_decl,type,
vd469: $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(leq_decl,type,
leq: $i > $i > $o ).
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(vd470_decl,type,
vd470: $i ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ vplus ) @ ( A @ vmul ) )
= ( C @ ( A @ vmul ) @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(125,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)],[28]) ).
thf(17,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(89,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(117,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(96,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,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(73,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)],[13]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).
thf(34,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( A @ vsucc )
!= ( B @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
thf(103,plain,
! [A: $i,B: $i] :
( B
!= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
( vd470
= ( vd473 @ ( vd471 @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(302)), 474, 0)') ).
thf(123,plain,
( vd470
= ( vd473 @ ( vd471 @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,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(43,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)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(55,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,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(58,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)],[9]) ).
thf(7,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(51,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(62,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vmul ) )
= ( B @ ( B @ ( A @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(24,axiom,
( ( vd469 @ ( vd470 @ vmul ) )
= ( vd469 @ ( vd473 @ ( vd471 @ vplus ) @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 0)') ).
thf(115,plain,
( ( vd469 @ ( vd470 @ vmul ) )
= ( vd469 @ ( vd473 @ ( vd471 @ vplus ) @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(120,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vmul ) )
= ( A @ ( B @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vmul ) @ vmul ) )
= ( C @ ( B @ vmul ) @ ( A @ vmul ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(93,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)],[19]) ).
thf(1,conjecture,
( ( vd469 @ ( vd473 @ ( vd471 @ vplus ) @ vmul ) )
= ( vd469 @ ( vd473 @ vmul ) @ ( vd469 @ ( vd471 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq_conjunct2(conseq(302)), 475, 1)') ).
thf(2,negated_conjecture,
( ( vd469 @ ( vd473 @ ( vd471 @ vplus ) @ vmul ) )
!= ( vd469 @ ( vd473 @ vmul ) @ ( vd469 @ ( vd471 @ vmul ) @ vplus ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
( ( vd469 @ ( vd473 @ ( vd471 @ vplus ) @ vmul ) )
!= ( vd469 @ ( vd473 @ vmul ) @ ( vd469 @ ( vd471 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
vd471 @ ( vd470 @ greater ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(302), 472, 0)') ).
thf(92,plain,
vd471 @ ( vd470 @ greater ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,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(65,plain,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(76,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(5,axiom,
! [A: $i] :
( ( A @ vsucc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(39,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,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(67,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(31,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(99,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,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(87,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,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(107,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)],[23]) ).
thf(15,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(79,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)],[15]) ).
thf(133,plain,
$false,
inference(e,[status(thm)],[125,89,117,96,73,34,103,123,43,55,58,51,62,115,120,93,29,92,65,76,39,67,31,99,87,107,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM851+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % 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 : n001.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 04:18:57 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.41/1.20 % [INFO] Parsing done (204ms).
% 1.41/1.22 % [INFO] Running in sequential loop mode.
% 2.07/1.60 % [INFO] eprover registered as external prover.
% 2.07/1.61 % [INFO] Scanning for conjecture ...
% 2.25/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 2.25/1.78 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.43/1.84 % [INFO] Problem is first-order (TPTP FOF).
% 2.43/1.85 % [INFO] Type checking passed.
% 2.43/1.86 % [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 ...
% 4.44/2.69 % External prover 'e' found a proof!
% 4.44/2.69 % [INFO] Killing All external provers ...
% 4.44/2.70 % Time passed: 2146ms (effective reasoning time: 1473ms)
% 4.44/2.70 % 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)>
% 4.83/2.70 % Axioms used in derivation (26): ass(cond(6, 0), 0), def(cond(conseq(axiom(3)), 11), 1), ass(cond(goal(88), 0), 1), ass(cond(270, 0), 0), ass(cond(goal(88), 0), 2), ass(cond(goal(88), 0), 0), ass(cond(281, 0), 0), ass(cond(12, 0), 0), ass(cond(43, 0), 0), ass(cond(81, 0), 0), qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 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(73, 0), 0), holds(antec(302), 472, 0), ass(cond(20, 0), 0), ass(cond(253, 0), 0), holds(conseq_conjunct1(conseq(302)), 474, 0), ass(cond(261, 0), 0), ass(cond(52, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0), ass(cond(290, 0), 0), ass(cond(61, 0), 0), holds(conseq_conjunct2(conseq(302)), 475, 0), ass(cond(241, 0), 0)
% 4.83/2.70 % No. of inferences in proof: 56
% 4.83/2.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2146 ms resp. 1473 ms w/o parsing
% 4.83/2.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.83/2.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------