%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM667^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : 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 08:17:56 AM UTC 2026
% Result : Theorem 4.89s 2.53s
% Output : Refutation 4.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 47 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 231 ( 60 ~; 35 |; 2 &; 118 @)
% ( 0 <=>; 16 =>; 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 : 25 ( 0 ^; 25 !; 0 ?; 25 :)
% 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/sandbox/benchmark/theBenchmark.p',l) ).
thf(13,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( ( less @ x @ y )
| ( x = y ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
( ( y = x )
| ( less @ x @ y ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(4,axiom,
( ~ ( less @ y @ z )
=> ( y = z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(16,plain,
( ~ ( less @ y @ z )
=> ( y = z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
( ( less @ y @ z )
| ( y = z ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
( ( z = y )
| ( less @ y @ z ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(1,conjecture,
( ~ ( less @ x @ z )
=> ( x = z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz17) ).
thf(2,negated_conjecture,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( ~ ( less @ x @ z )
=> ( x = z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ~ ( less @ x @ z )
& ( x != z ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
~ ( less @ x @ z ),
inference(cnfConj,[status(thm)],[9]) ).
thf(81,plain,
( ( z = y )
| ~ $true
| ( ( less @ y @ z )
!= ( less @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[18,10]) ).
thf(82,plain,
( ( z = y )
| ( ( less @ y @ z )
!= ( less @ x @ z ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(106,plain,
( ( z = y )
| ( y != x )
| ( z != z ) ),
inference(simp,[status(thm)],[82]) ).
thf(109,plain,
( ( z = y )
| ( y != x ) ),
inference(simp,[status(thm)],[106]) ).
thf(11,plain,
x != z,
inference(cnfConj,[status(thm)],[9]) ).
thf(12,plain,
z != x,
inference(lifteq,[status(thm)],[11]) ).
thf(114,plain,
( ( y != x )
| ( y != x )
| ( z != z ) ),
inference(paramod_ordered,[status(thm)],[109,12]) ).
thf(115,plain,
( ( y != x )
| ( z != z ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
y != x,
inference(pattern_uni,[status(thm)],[115:[]]) ).
thf(132,plain,
less @ x @ y,
inference(simplifyReflect,[status(thm)],[15,116]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ~ ( less @ A @ B )
=> ( A = B ) )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16a) ).
thf(20,plain,
! [A: nat,B: nat,C: nat] :
( ( ~ ( less @ A @ B )
=> ( A = B ) )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [A: nat,B: nat] :
( ( ~ ( less @ A @ B )
=> ( A = B ) )
=> ! [C: nat] :
( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [C: nat,B: nat,A: nat] :
( ( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( less @ A @ C ) )
& ( ( A != B )
| ~ ( less @ B @ C )
| ( less @ A @ C ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( less @ A @ C ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(40,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ~ $true
| ( ( less @ A @ C )
!= ( less @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[23,10]) ).
thf(41,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( ( less @ A @ C )
!= ( less @ x @ z ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
! [A: nat] :
( ~ ( less @ x @ A )
| ~ ( less @ A @ z ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(59,plain,
! [A: nat] :
( ~ ( less @ x @ A )
| ~ ( less @ A @ z ) ),
inference(simp,[status(thm)],[42]) ).
thf(136,plain,
! [A: nat] :
( ~ $true
| ~ ( less @ A @ z )
| ( ( less @ x @ y )
!= ( less @ x @ A ) ) ),
inference(paramod_ordered,[status(thm)],[132,59]) ).
thf(137,plain,
! [A: nat] :
( ~ ( less @ A @ z )
| ( ( less @ x @ y )
!= ( less @ x @ A ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
~ ( less @ y @ z ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( y ))]]) ).
thf(34,plain,
( ( y = x )
| ~ $true
| ( ( less @ x @ z )
!= ( less @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[15,10]) ).
thf(35,plain,
( ( y = x )
| ( ( less @ x @ z )
!= ( less @ x @ y ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(38,plain,
( ( y = x )
| ( x != x )
| ( z != y ) ),
inference(simp,[status(thm)],[35]) ).
thf(39,plain,
( ( y = x )
| ( z != y ) ),
inference(simp,[status(thm)],[38]) ).
thf(131,plain,
z != y,
inference(simplifyReflect,[status(thm)],[39,116]) ).
thf(133,plain,
less @ y @ z,
inference(simplifyReflect,[status(thm)],[18,131]) ).
thf(170,plain,
~ $true,
inference(rewrite,[status(thm)],[138,133]) ).
thf(171,plain,
$false,
inference(simp,[status(thm)],[170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM667^1 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.09/0.20 % Computer : n007.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 12:31:25 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.97 % [INFO] Parsing done (180ms).
% 1.24/0.99 % [INFO] Running in sequential loop mode.
% 1.85/1.38 % [INFO] eprover registered as external prover.
% 1.85/1.39 % [INFO] Scanning for conjecture ...
% 2.06/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.21/1.50 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.21/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.53 % [INFO] Type checking passed.
% 2.21/1.54 % [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 ...
% 4.89/2.53 % [INFO] Killing All external provers ...
% 4.89/2.53 % Time passed: 2179ms (effective reasoning time: 1537ms)
% 4.89/2.53 % 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)>
% 4.89/2.53 % Axioms used in derivation (3): l, k, satz16a
% 4.89/2.53 % No. of inferences in proof: 43
% 4.89/2.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2179 ms resp. 1537 ms w/o parsing
% 4.89/2.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.89/2.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------