%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM663^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : n013.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 08:17:55 AM UTC 2026
% Result : Theorem 5.67s 2.95s
% Output : Refutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 63 ( 13 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 144 ( 30 ~; 16 |; 0 &; 90 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 0 ^; 22 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(z_decl,type,
z: nat ).
thf(less_decl,type,
less: nat > nat > $o ).
thf(3,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(8,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
( ( less @ x @ y )
| ( x = y ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
( ( y = x )
| ( less @ x @ y ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(4,axiom,
less @ y @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(11,plain,
less @ y @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
less @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
thf(2,negated_conjecture,
~ ( less @ x @ z ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( less @ x @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ~ $true
| ( ( less @ y @ z )
!= ( less @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(17,plain,
( ( less @ y @ z )
!= ( less @ x @ z ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
( ( y != x )
| ( z != z ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
y != x,
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
less @ x @ y,
inference(simplifyReflect,[status(thm)],[10,19]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(13,plain,
! [A: nat,B: nat,C: nat] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,plain,
! [A: nat,B: nat] :
( ( less @ A @ B )
=> ! [C: nat] :
( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( less @ A @ C ) ),
inference(cnf,[status(esa)],[14]) ).
thf(31,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ~ $true
| ( ( less @ A @ C )
!= ( less @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[15,7]) ).
thf(32,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( ( less @ A @ C )
!= ( less @ x @ z ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(33,plain,
! [A: nat] :
( ~ ( less @ x @ A )
| ~ ( less @ A @ z ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(48,plain,
! [A: nat] :
( ~ ( less @ x @ A )
| ~ ( less @ A @ z ) ),
inference(simp,[status(thm)],[33]) ).
thf(79,plain,
! [A: nat] :
( ~ $true
| ~ ( less @ A @ z )
| ( ( less @ x @ y )
!= ( less @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[20,48]) ).
thf(80,plain,
! [A: nat] :
( ~ ( less @ A @ z )
| ( ( less @ x @ y )
!= ( less @ x @ A ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(81,plain,
~ ( less @ y @ z ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( y ))]]) ).
thf(148,plain,
~ $true,
inference(rewrite,[status(thm)],[81,11]) ).
thf(149,plain,
$false,
inference(simp,[status(thm)],[148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM663^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.10 % 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
% 0.09/0.26 % Computer : n013.cluster.edu
% 0.09/0.26 % Model : x86_64 x86_64
% 0.09/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.26 % Memory : 8046.5625MB
% 0.09/0.26 % OS : Linux 6.8.0-71-generic
% 0.09/0.26 % CPULimit : 300
% 0.09/0.26 % WCLimit : 300
% 0.09/0.26 % DateTime : Tue Sep 29 12:32:36 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 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
% 1.13/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.72/1.20 % [INFO] Parsing done (196ms).
% 1.72/1.21 % [INFO] Running in sequential loop mode.
% 2.34/1.66 % [INFO] eprover registered as external prover.
% 2.34/1.67 % [INFO] Scanning for conjecture ...
% 2.58/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.58/1.78 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.76/1.80 % [INFO] Problem is higher-order (TPTP THF).
% 2.76/1.81 % [INFO] Type checking passed.
% 2.76/1.81 % [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 ...
% 5.67/2.95 % [INFO] Killing All external provers ...
% 5.67/2.95 % Time passed: 2484ms (effective reasoning time: 1727ms)
% 5.67/2.95 % 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)>
% 5.67/2.95 % Axioms used in derivation (3): l, k, satz15
% 5.67/2.95 % No. of inferences in proof: 27
% 5.67/2.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2484 ms resp. 1727 ms w/o parsing
% 5.67/3.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.67/3.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------