%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM664^1 : 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 : n011.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 4.16s 1.93s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 13 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 134 ( 25 ~; 15 |; 0 &; 86 @)
% ( 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 : 21 ( 0 ^; 21 !; 0 ?; 21 :)
% 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(4,axiom,
( ~ ( less @ y @ z )
=> ( y = z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(9,plain,
( ~ ( less @ y @ z )
=> ( y = z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
( ( less @ y @ z )
| ( y = z ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
( ( z = y )
| ( less @ y @ z ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(3,axiom,
less @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(8,plain,
less @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
less @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16b) ).
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 @ x @ z )
!= ( less @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[8,7]) ).
thf(17,plain,
( ( less @ x @ z )
!= ( less @ x @ y ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
( ( x != x )
| ( z != y ) ),
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
z != y,
inference(simp,[status(thm)],[18]) ).
thf(20,plain,
less @ y @ z,
inference(simplifyReflect,[status(thm)],[11,19]) ).
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(28,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ $true
| ( less @ A @ C )
| ( ( less @ y @ z )
!= ( less @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,15]) ).
thf(29,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( less @ A @ C )
| ( ( less @ y @ z )
!= ( less @ B @ C ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(30,plain,
! [A: nat] :
( ~ ( less @ A @ y )
| ( less @ A @ z ) ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(55,plain,
! [A: nat] :
( ~ ( less @ A @ y )
| ~ $true
| ( ( less @ A @ z )
!= ( less @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[30,7]) ).
thf(56,plain,
! [A: nat] :
( ~ ( less @ A @ y )
| ( ( less @ A @ z )
!= ( less @ x @ z ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(57,plain,
~ ( less @ x @ y ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( x ))]]) ).
thf(77,plain,
~ $true,
inference(rewrite,[status(thm)],[57,8]) ).
thf(78,plain,
$false,
inference(simp,[status(thm)],[77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM664^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.11 % 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
% 0.24/0.29 % Computer : n011.cluster.edu
% 0.24/0.29 % Model : x86_64 x86_64
% 0.24/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.29 % Memory : 8046.5625MB
% 0.24/0.29 % OS : Linux 6.8.0-71-generic
% 0.24/0.29 % CPULimit : 300
% 0.24/0.29 % WCLimit : 300
% 0.24/0.29 % DateTime : Tue Sep 29 12:33:46 UTC 2026
% 0.24/0.29 % CPUTime :
% 0.24/0.30 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
% 0.95/0.73 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.85 % [INFO] Parsing done (108ms).
% 1.23/0.85 % [INFO] Running in sequential loop mode.
% 1.71/1.08 % [INFO] eprover registered as external prover.
% 1.71/1.08 % [INFO] Scanning for conjecture ...
% 1.71/1.14 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.99/1.16 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.99/1.18 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.18 % [INFO] Type checking passed.
% 1.99/1.18 % [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 ...
% 4.16/1.93 % [INFO] Killing All external provers ...
% 4.16/1.93 % Time passed: 1505ms (effective reasoning time: 1070ms)
% 4.16/1.93 % 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)>
% 4.16/1.93 % Axioms used in derivation (3): k, l, satz15
% 4.16/1.93 % No. of inferences in proof: 26
% 4.16/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1505 ms resp. 1070 ms w/o parsing
% 4.16/1.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.16/1.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------