%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM667_8 : TPTP v9.3.1. Released v8.0.0.
% 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 : n001.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 08:09:32 AM UTC 2026
% Result : Theorem 5.45s 2.67s
% Output : Refutation 5.74s
% 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,
( ~ ( y @ ( x @ less ) )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(13,plain,
( ~ ( y @ ( x @ less ) )
=> ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( ( x = y )
| ( y @ ( x @ less ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
( ( y @ ( x @ less ) )
| ( y = x ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(4,axiom,
( ~ ( z @ ( y @ less ) )
=> ( y = z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(16,plain,
( ~ ( z @ ( y @ less ) )
=> ( y = z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
( ( y = z )
| ( z @ ( y @ less ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
( ( z @ ( y @ less ) )
| ( z = y ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(1,conjecture,
( ~ ( z @ ( x @ less ) )
=> ( x = z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz17) ).
thf(2,negated_conjecture,
~ ( ~ ( z @ ( x @ less ) )
=> ( x = z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( ~ ( z @ ( x @ less ) )
=> ( x = z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( x != z )
& ~ ( z @ ( x @ less ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
~ ( z @ ( x @ less ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(81,plain,
( ( ( z @ ( y @ less ) )
!= ( z @ ( x @ less ) ) )
| ~ $true
| ( z = y ) ),
inference(paramod_ordered,[status(thm)],[18,10]) ).
thf(82,plain,
( ( ( z @ ( y @ less ) )
!= ( z @ ( x @ less ) ) )
| ( z = y ) ),
inference(simp,[status(thm)],[81]) ).
thf(106,plain,
( ( z != z )
| ( y != x )
| ( z = y ) ),
inference(simp,[status(thm)],[82]) ).
thf(109,plain,
( ( y != x )
| ( z = y ) ),
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,
( ( z != z )
| ( y != x )
| ( y != x ) ),
inference(paramod_ordered,[status(thm)],[109,12]) ).
thf(115,plain,
( ( z != z )
| ( y != x ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
y != x,
inference(pattern_uni,[status(thm)],[115:[]]) ).
thf(132,plain,
y @ ( x @ less ),
inference(simplifyReflect,[status(thm)],[15,116]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( ~ ( B @ ( A @ less ) )
=> ( A = B ) )
=> ( ( C @ ( B @ less ) )
=> ( C @ ( A @ less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
thf(20,plain,
! [A: nat,B: nat,C: nat] :
( ( ~ ( B @ ( A @ less ) )
=> ( A = B ) )
=> ( ( C @ ( B @ less ) )
=> ( C @ ( A @ less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,plain,
! [A: nat,B: nat] :
( ( ~ ( B @ ( A @ less ) )
=> ( A = B ) )
=> ! [C: nat] :
( ( C @ ( B @ less ) )
=> ( C @ ( A @ less ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [C: nat,B: nat,A: nat] :
( ( ( C @ ( A @ less ) )
| ~ ( C @ ( B @ less ) )
| ( A != B ) )
& ( ( C @ ( A @ less ) )
| ~ ( C @ ( B @ less ) )
| ~ ( B @ ( A @ less ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: nat,B: nat,A: nat] :
( ( C @ ( A @ less ) )
| ~ ( C @ ( B @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(40,plain,
! [C: nat,B: nat,A: nat] :
( ( ( C @ ( A @ less ) )
!= ( z @ ( x @ less ) ) )
| ~ $true
| ~ ( C @ ( B @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(paramod_ordered,[status(thm)],[23,10]) ).
thf(41,plain,
! [C: nat,B: nat,A: nat] :
( ( ( C @ ( A @ less ) )
!= ( z @ ( x @ less ) ) )
| ~ ( C @ ( B @ less ) )
| ~ ( B @ ( A @ less ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
! [A: nat] :
( ~ ( z @ ( A @ less ) )
| ~ ( A @ ( x @ less ) ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( x )),bind(B,$thf( B )),bind(C,$thf( z ))]]) ).
thf(59,plain,
! [A: nat] :
( ~ ( z @ ( A @ less ) )
| ~ ( A @ ( x @ less ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(136,plain,
! [A: nat] :
( ( ( y @ ( x @ less ) )
!= ( A @ ( x @ less ) ) )
| ~ ( z @ ( A @ less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[132,59]) ).
thf(137,plain,
! [A: nat] :
( ( ( y @ ( x @ less ) )
!= ( A @ ( x @ less ) ) )
| ~ ( z @ ( A @ less ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
~ ( z @ ( y @ less ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( y ))]]) ).
thf(34,plain,
( ( ( z @ ( x @ less ) )
!= ( y @ ( x @ less ) ) )
| ~ $true
| ( y = x ) ),
inference(paramod_ordered,[status(thm)],[15,10]) ).
thf(35,plain,
( ( ( z @ ( x @ less ) )
!= ( y @ ( x @ less ) ) )
| ( y = x ) ),
inference(simp,[status(thm)],[34]) ).
thf(38,plain,
( ( z != y )
| ( x != x )
| ( y = x ) ),
inference(simp,[status(thm)],[35]) ).
thf(39,plain,
( ( z != y )
| ( y = x ) ),
inference(simp,[status(thm)],[38]) ).
thf(131,plain,
z != y,
inference(simplifyReflect,[status(thm)],[39,116]) ).
thf(133,plain,
z @ ( y @ less ),
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
% 0.00/0.05 % Problem : NUM667_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.12 % 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
% 0.24/0.51 % Computer : n001.cluster.edu
% 0.24/0.51 % Model : x86_64 x86_64
% 0.24/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.51 % Memory : 8046.5625MB
% 0.24/0.51 % OS : Linux 6.8.0-71-generic
% 0.24/0.51 % CPULimit : 300
% 0.24/0.51 % WCLimit : 300
% 0.24/0.51 % DateTime : Sat Sep 26 03:46:13 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 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
% 0.91/1.03 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.20 % [INFO] Parsing done (167ms).
% 1.51/1.21 % [INFO] Running in sequential loop mode.
% 2.05/1.58 % [INFO] eprover registered as external prover.
% 2.05/1.58 % [INFO] Scanning for conjecture ...
% 2.30/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.51/1.70 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.51/1.73 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.51/1.73 % [INFO] Type checking passed.
% 2.51/1.74 % [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 ...
% 5.45/2.66 % [INFO] Killing All external provers ...
% 5.45/2.66 % Time passed: 2004ms (effective reasoning time: 1441ms)
% 5.45/2.66 % 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)>
% 5.45/2.66 % Axioms used in derivation (3): l, k, satz16a
% 5.45/2.66 % No. of inferences in proof: 43
% 5.45/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2004 ms resp. 1441 ms w/o parsing
% 5.74/2.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.74/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------