%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM847+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 : n006.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 08:10:10 AM UTC 2026
% Result : Theorem 4.20s 2.58s
% Output : Refutation 4.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 41 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 314 ( 6 ~; 0 |; 4 &; 298 @)
% ( 0 <=>; 6 =>; 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 : 14 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 38 ( 0 ^; 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vmul_decl,type,
vmul: $i > $i > $i ).
thf(vd436_decl,type,
vd436: $i ).
thf(vd437_decl,type,
vd437: $i ).
thf(vd439_decl,type,
vd439: $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(17,axiom,
( ( vd436 @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) )
= ( v1 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(284, 438, 2)') ).
thf(69,plain,
( ( vd436 @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) )
= ( v1 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(14,axiom,
( ( vd436 @ ( vd439 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) @ vplus ) )
= ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 2)') ).
thf(56,plain,
( ( vd436 @ ( vd439 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) @ vplus ) )
= ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
( ( vd437 @ vsucc @ ( vd436 @ vmul ) )
= ( vd436 @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(284, 438, 1)') ).
thf(37,plain,
( ( vd437 @ vsucc @ ( vd436 @ vmul ) )
= ( vd436 @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
( ( vd439 @ ( vd437 @ vplus ) @ vsucc @ ( vd436 @ vmul ) )
= ( vd436 @ ( vd439 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 1)') ).
thf(74,plain,
( ( vd439 @ ( vd437 @ vplus ) @ vsucc @ ( vd436 @ vmul ) )
= ( vd436 @ ( vd439 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(66,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(7,axiom,
( ( vd439 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) )
= ( vd439 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(285, 440, 0)') ).
thf(35,plain,
( ( vd439 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) )
= ( vd439 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(58,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)],[15]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(234, 0), 0)') ).
thf(47,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ greater ) )
=> ( v1 @ ( B @ vplus ) @ ( A @ geq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
( ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) @ vplus ) )
= ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ vplus ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 3)') ).
thf(2,negated_conjecture,
( ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) @ vplus ) )
!= ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ vplus ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
( ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) @ vplus ) )
!= ( vd436 @ ( vd439 @ ( vd436 @ vmul ) @ vplus ) @ ( vd437 @ ( vd436 @ vmul ) @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(241, 0), 0)') ).
thf(33,plain,
! [A: $i,B: $i] :
( ( v1 @ ( B @ vplus ) @ ( A @ less ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(253, 0), 0)') ).
thf(71,plain,
! [A: $i] :
( ( A @ ( v1 @ vmul ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(13,axiom,
( ( vd439 @ vsucc @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) )
= ( vd439 @ ( vd437 @ vplus ) @ vsucc @ ( vd436 @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(286, 441, 0)') ).
thf(54,plain,
( ( vd439 @ vsucc @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) )
= ( vd439 @ ( vd437 @ vplus ) @ vsucc @ ( vd436 @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
( ( v1 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) )
= ( vd437 @ vsucc @ ( vd436 @ vmul ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(284, 438, 0)') ).
thf(49,plain,
( ( v1 @ ( vd437 @ vplus ) @ ( vd436 @ vmul ) )
= ( vd437 @ vsucc @ ( vd436 @ vmul ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).
thf(76,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vmul ) )
= A )
& ( ( B @ vsucc @ ( A @ vmul ) )
= ( A @ ( B @ ( A @ vmul ) @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
thf(39,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)],[9]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ vsucc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(26,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(23,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(30,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(51,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(79,plain,
$false,
inference(e,[status(thm)],[69,56,37,74,66,35,58,47,21,33,71,54,49,76,39,26,23,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM847+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % 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
% 0.15/0.40 % Computer : n006.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 04:12:41 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.20 % [INFO] Parsing done (204ms).
% 1.40/1.21 % [INFO] Running in sequential loop mode.
% 2.11/1.62 % [INFO] eprover registered as external prover.
% 2.11/1.63 % [INFO] Scanning for conjecture ...
% 2.31/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.50/1.80 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.50/1.85 % [INFO] Problem is first-order (TPTP FOF).
% 2.50/1.86 % [INFO] Type checking passed.
% 2.50/1.87 % [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 ...
% 4.20/2.58 % External prover 'e' found a proof!
% 4.20/2.58 % [INFO] Killing All external provers ...
% 4.20/2.58 % Time passed: 2035ms (effective reasoning time: 1357ms)
% 4.20/2.58 % 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)>
% 4.20/2.58 % Axioms used in derivation (18): qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), holds(286, 441, 1), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(20, 0), 0), holds(285, 440, 0), ass(cond(253, 0), 0), ass(cond(61, 0), 0), ass(cond(241, 0), 0), ass(cond(12, 0), 0), ass(cond(43, 0), 0), holds(284, 438, 1), holds(286, 441, 2), holds(284, 438, 2), holds(286, 441, 0), holds(284, 438, 0), ass(cond(52, 0), 0), ass(cond(234, 0), 0), ass(cond(33, 0), 0)
% 4.20/2.58 % No. of inferences in proof: 40
% 4.20/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2035 ms resp. 1357 ms w/o parsing
% 4.46/2.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.46/2.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------