%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM835+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 08:10:06 AM UTC 2026
% Result : Theorem 3.99s 2.54s
% Output : Refutation 4.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 24
% Syntax : Number of formulae : 50 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 106 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 333 ( 18 ~; 12 |; 3 &; 247 @)
% ( 1 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 52 !; 12 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(vd165_decl,type,
vd165: $i ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vd151_decl,type,
vd151: $i ).
thf(v1_decl,type,
v1: $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(vskolem2_decl,type,
vskolem2: $i > $i ).
thf(m_decl,type,
m: $i > $o ).
thf(vskolem3_decl,type,
vskolem3: $i ).
thf(23,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( vd165 @ vsucc @ m ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 0)') ).
thf(115,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( vd165 @ vsucc @ m ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
( ( vd151 = vd165 )
=> ( vd165 @ vsucc @ m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 0)') ).
thf(42,plain,
( ( vd151 = vd165 )
=> ( vd165 @ vsucc @ m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i] :
( ( vd165
= ( A @ ( vd151 @ vplus ) ) )
=> ( vd165 @ vsucc @ m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 0)') ).
thf(93,plain,
! [A: $i] :
( ( vd165
= ( A @ ( vd151 @ vplus ) ) )
=> ( vd165 @ vsucc @ m ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(15,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A = v1 )
=> ( vd165 @ vsucc @ m ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 6)') ).
thf(89,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A = v1 )
=> ( vd165 @ vsucc @ m ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ vsucc )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).
thf(38,plain,
! [A: $i] :
( ( A @ vsucc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(21,axiom,
! [A: $i] :
( ( vd165
= ( A @ ( vd151 @ vplus ) ) )
=> ( ( vd165 @ vsucc )
= ( A @ ( vd151 @ vplus ) @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 2)') ).
thf(109,plain,
! [A: $i] :
( ( vd165
= ( A @ ( vd151 @ vplus ) ) )
=> ( ( vd165 @ vsucc )
= ( A @ ( vd151 @ vplus ) @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
thf(73,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ vplus ) )
= ( B @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,axiom,
( ( vd151 = vd165 )
=> ( ( vd165 @ vsucc )
= ( v1 @ ( vd165 @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 2)') ).
thf(45,plain,
( ( vd151 = vd165 )
=> ( ( vd165 @ vsucc )
= ( v1 @ ( vd165 @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
thf(118,plain,
! [A: $i] :
( ( A @ ( v1 @ vplus ) )
= ( A @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(14,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( vd151
= ( vskolem3 @ ( v1 @ vplus ) @ ( vd165 @ vplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 3)') ).
thf(86,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( vd151
= ( vskolem3 @ ( v1 @ vplus ) @ ( vd165 @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,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)],[11]) ).
thf(19,axiom,
! [A: $i] :
( ( vd165
= ( A @ ( vd151 @ vplus ) ) )
=> ( ( A @ ( vd151 @ vplus ) @ vsucc )
= ( A @ vsucc @ ( vd151 @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 2), 1)') ).
thf(103,plain,
! [A: $i] :
( ( vd165
= ( A @ ( vd151 @ vplus ) ) )
=> ( ( A @ ( vd151 @ vplus ) @ vsucc )
= ( A @ vsucc @ ( vd151 @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).
thf(35,plain,
! [A: $i] :
( ( A != v1 )
=> ( A
= ( A @ vskolem2 @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( ( vskolem3 @ ( v1 @ ( vd165 @ vplus ) @ vplus ) )
= ( vskolem3 @ ( vd165 @ vsucc @ vplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 1)') ).
thf(112,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( ( vskolem3 @ ( v1 @ ( vd165 @ vplus ) @ vplus ) )
= ( vskolem3 @ ( vd165 @ vsucc @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ m )
<=> ( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(105), 0), 1)') ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) )
=> ( B @ m ) )
& ( ( B @ m )
=> ( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
( ( vd151 = vd165 )
| ? [A: $i] :
( vd151
= ( A @ ( vd165 @ vplus ) ) )
| ? [A: $i] :
( vd165
= ( A @ ( vd151 @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dis(case_distinction(conseq(110)))') ).
thf(2,negated_conjecture,
~ ( ( vd151 = vd165 )
| ? [A: $i] :
( vd151
= ( A @ ( vd165 @ vplus ) ) )
| ? [A: $i] :
( vd165
= ( A @ ( vd151 @ vplus ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(26,plain,
~ ( ( vd151 = vd165 )
| ? [A: $i] :
( vd151
= ( A @ ( vd165 @ vplus ) ) )
| ? [A: $i] :
( vd165
= ( A @ ( vd151 @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A = v1 )
=> ( vd151
= ( v1 @ ( vd165 @ vplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 8)') ).
thf(82,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A = v1 )
=> ( vd151
= ( v1 @ ( vd165 @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( ( vskolem3 @ ( v1 @ vplus ) @ ( vd165 @ vplus ) )
= ( vskolem3 @ ( v1 @ ( vd165 @ vplus ) @ vplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 2)') ).
thf(79,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( ( vskolem3 @ ( v1 @ vplus ) @ ( vd165 @ vplus ) )
= ( vskolem3 @ ( v1 @ ( vd165 @ vplus ) @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
( ( vd151 = vd165 )
=> ( ( v1 @ ( vd165 @ vplus ) )
= ( v1 @ ( vd151 @ vplus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 0), 1)') ).
thf(62,plain,
( ( vd151 = vd165 )
=> ( ( v1 @ ( vd165 @ vplus ) )
= ( v1 @ ( vd151 @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( A
= ( vskolem3 @ vsucc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 5)') ).
thf(100,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( A
= ( vskolem3 @ vsucc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,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(106,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ vsucc @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A = v1 )
=> ( ( v1 @ ( vd165 @ vplus ) )
= ( vd165 @ vsucc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 7)') ).
thf(121,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A = v1 )
=> ( ( v1 @ ( vd165 @ vplus ) )
= ( vd165 @ vsucc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,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(65,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)],[9]) ).
thf(17,axiom,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( ( vskolem3 @ vsucc )
= ( vskolem3 @ ( v1 @ vplus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(110), 1), 4)') ).
thf(97,plain,
! [A: $i] :
( ( vd151
= ( A @ ( vd165 @ vplus ) ) )
=> ( ( A != v1 )
=> ( ( vskolem3 @ vsucc )
= ( vskolem3 @ ( v1 @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(125,plain,
$false,
inference(e,[status(thm)],[115,42,93,89,38,109,73,45,118,86,76,103,35,112,48,26,82,79,62,100,106,121,65,97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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
% 0.15/0.41 % Computer : n009.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 04:11:15 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.19 % [INFO] Parsing done (198ms).
% 1.37/1.21 % [INFO] Running in sequential loop mode.
% 2.07/1.60 % [INFO] eprover registered as external prover.
% 2.07/1.61 % [INFO] Scanning for conjecture ...
% 2.22/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 23 axioms. Running axiom selection ...
% 2.22/1.79 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.39/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.84 % [INFO] Type checking passed.
% 2.39/1.84 % [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 ...
% 3.99/2.53 % External prover 'e' found a proof!
% 3.99/2.53 % [INFO] Killing All external provers ...
% 3.99/2.54 % Time passed: 1983ms (effective reasoning time: 1323ms)
% 3.99/2.54 % 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)>
% 3.99/2.54 % Axioms used in derivation (23): ass(cond(conseq(110), 2), 0), def(cond(conseq(105), 0), 1), ass(cond(conseq(110), 2), 1), ass(cond(conseq(110), 1), 5), ass(cond(conseq(110), 1), 6), ass(cond(33, 0), 0), ass(cond(61, 0), 0), ass(cond(conseq(110), 0), 0), ass(cond(12, 0), 0), ass(cond(conseq(110), 1), 1), ass(cond(conseq(110), 1), 0), ass(cond(conseq(110), 2), 2), ass(cond(conseq(110), 1), 3), ass(cond(conseq(110), 1), 7), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(conseq(110), 1), 4), ass(cond(20, 0), 0), ass(cond(conseq(110), 0), 1), ass(cond(conseq(110), 0), 2), ass(cond(52, 0), 0), ass(cond(conseq(110), 1), 2), ass(cond(43, 0), 0), ass(cond(conseq(110), 1), 8)
% 3.99/2.54 % No. of inferences in proof: 50
% 3.99/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1983 ms resp. 1323 ms w/o parsing
% 4.26/2.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.26/2.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------