%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM656^1 : 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 : n016.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 08:17:54 AM UTC 2026
% Result : Theorem 3.88s 2.20s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 25 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 173 ( 53 ~; 15 |; 2 &; 84 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_decl,type,
x: nat ).
thf(y_decl,type,
y: nat ).
thf(more_decl,type,
more: nat > nat > $o ).
thf(less_decl,type,
less: nat > nat > $o ).
thf(1,conjecture,
~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10g) ).
thf(2,negated_conjecture,
~ ~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( less @ x @ y )
| ( x = y ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( y = x )
| ( less @ x @ y ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(3,axiom,
more @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(10,plain,
more @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: nat,B: nat] :
~ ( ( ( A = B )
=> ~ ( more @ A @ B ) )
=> ~ ~ ( ( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ( ( less @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10b) ).
thf(12,plain,
! [A: nat,B: nat] :
~ ( ( ( A = B )
=> ~ ( more @ A @ B ) )
=> ( ( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ( ( less @ A @ B )
=> ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
~ ( ! [A: nat,B: nat] :
( ( A = B )
=> ~ ( more @ A @ B ) )
=> ( ! [A: nat,B: nat] :
( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ! [A: nat,B: nat] :
( ( less @ A @ B )
=> ( A != B ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(14,plain,
! [F: nat,E: nat,D: nat,C: nat,B: nat,A: nat] :
( ( ( A != B )
| ~ ( more @ A @ B ) )
& ( ~ ( more @ C @ D )
| ~ ( less @ C @ D ) )
& ( ~ ( less @ E @ F )
| ( E != F ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(16,plain,
! [B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( less @ A @ B ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(20,plain,
! [B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( less @ A @ B ) ),
inference(simp,[status(thm)],[16]) ).
thf(27,plain,
! [B: nat,A: nat] :
( ~ $true
| ~ ( less @ A @ B )
| ( ( more @ x @ y )
!= ( more @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,20]) ).
thf(28,plain,
! [B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( ( more @ x @ y )
!= ( more @ A @ B ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
~ ( less @ x @ y ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(30,plain,
( ( y = x )
| $false ),
inference(rewrite,[status(thm)],[9,29]) ).
thf(31,plain,
y = x,
inference(simp,[status(thm)],[30]) ).
thf(15,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( more @ A @ B ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( more @ A @ B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(19,plain,
! [A: nat] :
~ ( more @ A @ A ),
inference(simp,[status(thm)],[18]) ).
thf(23,plain,
! [A: nat] :
( ~ $true
| ( ( more @ x @ y )
!= ( more @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,19]) ).
thf(24,plain,
! [A: nat] :
( ( more @ x @ y )
!= ( more @ A @ A ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [A: nat] :
( ( x != A )
| ( y != A ) ),
inference(simp,[status(thm)],[24]) ).
thf(26,plain,
y != x,
inference(simp,[status(thm)],[25]) ).
thf(32,plain,
$false,
inference(simplifyReflect,[status(thm)],[31,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM656^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % 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
% 0.10/0.18 % Computer : n016.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 12:37:04 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.92/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/0.98 % [INFO] Parsing done (189ms).
% 1.26/0.99 % [INFO] Running in sequential loop mode.
% 1.87/1.39 % [INFO] eprover registered as external prover.
% 1.87/1.39 % [INFO] Scanning for conjecture ...
% 2.08/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.25/1.51 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.25/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.25/1.53 % [INFO] Type checking passed.
% 2.25/1.54 % [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 ...
% 3.75/2.20 % [INFO] Killing All external provers ...
% 3.88/2.20 % Time passed: 1875ms (effective reasoning time: 1201ms)
% 3.88/2.20 % 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)>
% 3.88/2.20 % Axioms used in derivation (2): m, satz10b
% 3.88/2.20 % No. of inferences in proof: 27
% 3.88/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1875 ms resp. 1201 ms w/o parsing
% 3.88/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.88/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------