%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM802^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 : Wed Sep 30 08:18:13 AM UTC 2026
% Result : Theorem 3.82s 2.22s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 1 def)
% Number of atoms : 26 ( 14 equ; 3 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 101 ( 17 ~; 5 |; 6 &; 61 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 1 ^; 14 !; 6 ?; 22 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_2_decl,type,
c_2: $i ).
thf(absval_decl,type,
absval: $i > $i ).
thf(c0_decl,type,
c0: $i ).
thf(c_less__decl,type,
c_less_: $i > $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $o] :
@+[B: $i] : ( A @ ( absval @ B ) ) ) ) ).
thf(1,conjecture,
( ( c_less_ @ c_2 @ c0 )
=> ( ! [A: $i,B: $i] :
( ( c_less_ @ A @ c0 )
=> ( A
!= ( absval @ B ) ) )
=> ? [A: $i > $o] :
( ! [B: $i] :
~ ( A @ ( absval @ B ) )
& ( A @ c_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_8) ).
thf(2,negated_conjecture,
~ ( ( c_less_ @ c_2 @ c0 )
=> ( ! [A: $i,B: $i] :
( ( c_less_ @ A @ c0 )
=> ( A
!= ( absval @ B ) ) )
=> ? [A: $i > $o] :
( ! [B: $i] :
~ ( A @ ( absval @ B ) )
& ( A @ c_2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( c_less_ @ c_2 @ c0 )
=> ( ! [A: $i,B: $i] :
( ( c_less_ @ A @ c0 )
=> ( A
!= ( absval @ B ) ) )
=> ? [A: $i > $o] :
( ! [B: $i] :
~ ( A @ ( absval @ B ) )
& ( A @ c_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( c_less_ @ c_2 @ c0 )
=> ( ! [A: $i] :
( ( c_less_ @ A @ c0 )
=> ~ ? [B: $i] :
( A
= ( absval @ B ) ) )
=> ? [A: $i > $o] :
( ~ ? [B: $i] : ( A @ ( absval @ B ) )
& ( A @ c_2 ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [C: $i > $o,B: $i,A: $i] :
( ( c_less_ @ c_2 @ c0 )
& ( ~ ( c_less_ @ A @ c0 )
| ( A
!= ( absval @ B ) ) )
& ( ( C @ ( absval @ ( sk1 @ C ) ) )
| ~ ( C @ c_2 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
c_less_ @ c_2 @ c0,
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
! [A: $i > $o] :
( ( A @ ( absval @ ( sk1 @ A ) ) )
| ~ ( A @ c_2 ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
( ( c_2
= ( absval @ ( sk1 @ ( (=) @ $i @ c_2 ) ) ) )
| ( c_2 != c_2 ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (=) @ $i @ c_2 ))]]) ).
thf(13,plain,
( ( ( absval @ ( sk1 @ ( (=) @ $i @ c_2 ) ) )
= c_2 )
| ( c_2 != c_2 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(14,plain,
( ( absval @ ( sk1 @ ( (=) @ $i @ c_2 ) ) )
= c_2 ),
inference(simp,[status(thm)],[13]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[3,6,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM802^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.21 % Computer : n007.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 12:58:41 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (197ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 2.05/1.41 % [INFO] eprover registered as external prover.
% 2.05/1.42 % [INFO] Scanning for conjecture ...
% 2.24/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.56 % [INFO] Type checking passed.
% 2.24/1.56 % [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 ...
% 3.82/2.22 % External prover 'e' found a proof!
% 3.82/2.22 % [INFO] Killing All external provers ...
% 3.82/2.22 % Time passed: 1865ms (effective reasoning time: 1200ms)
% 3.82/2.22 % 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)>
% 3.82/2.22 % Axioms used in derivation (0):
% 3.82/2.22 % No. of inferences in proof: 11
% 3.82/2.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1865 ms resp. 1200 ms w/o parsing
% 3.82/2.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.82/2.27 % [INFO] Killing All external provers ...
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