%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM681^1 : 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 : n009.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 08:17:58 AM UTC 2026
% Result : Theorem 5.64s 2.43s
% Output : Refutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 112 ( 32 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 357 ( 58 ~; 30 |; 2 &; 242 @)
% ( 0 <=>; 25 =>; 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 : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 78 !; 0 ?; 78 :)
% 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(pl_decl,type,
pl: nat > nat > nat ).
thf(less_decl,type,
less: nat > nat > $o ).
thf(more_decl,type,
more: nat > nat > $o ).
thf(3,axiom,
( ( pl @ x @ z )
= ( pl @ y @ z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i) ).
thf(11,plain,
( ( pl @ x @ z )
= ( pl @ y @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
( ( pl @ y @ z )
= ( pl @ x @ z ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( more @ A @ B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10a) ).
thf(28,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( more @ A @ B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,plain,
! [B: nat,A: nat] :
( ( A = B )
| ( more @ A @ B )
| ( less @ A @ B ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: nat,A: nat] :
( ( A = B )
| ( more @ A @ B )
| ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(1,conjecture,
x = y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20b) ).
thf(2,negated_conjecture,
x != y,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
x != y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
y != x,
inference(lifteq,[status(thm)],[9]) ).
thf(53,plain,
! [B: nat,A: nat] :
( ( more @ A @ B )
| ( less @ A @ B )
| ( A != x )
| ( B != y ) ),
inference(paramod_ordered,[status(thm)],[30,10]) ).
thf(54,plain,
! [A: nat] :
( ( more @ A @ y )
| ( less @ A @ y )
| ( A != x ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( y ))]]) ).
thf(86,plain,
( ( more @ x @ y )
| ( less @ x @ y ) ),
inference(simp,[status(thm)],[54]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( less @ A @ B )
=> ( less @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19c) ).
thf(25,plain,
! [A: nat,B: nat,C: nat] :
( ( less @ A @ B )
=> ( less @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,plain,
! [A: nat,B: nat] :
( ( less @ A @ B )
=> ! [C: nat] : ( less @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(miniscope,[status(thm)],[25]) ).
thf(27,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( less @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(37,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( less @ ( pl @ A @ C ) @ ( pl @ x @ z ) )
| ( ( pl @ y @ z )
!= ( pl @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[12,27]) ).
thf(38,plain,
! [A: nat] :
( ~ ( less @ A @ y )
| ( less @ ( pl @ A @ z ) @ ( pl @ x @ z ) ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
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(14,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(15,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)],[14]) ).
thf(16,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)],[15]) ).
thf(19,plain,
! [B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(23,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(24,plain,
! [A: nat] :
~ ( less @ A @ A ),
inference(simp,[status(thm)],[23]) ).
thf(165,plain,
! [B: nat,A: nat] :
( ~ ( less @ A @ y )
| ~ $true
| ( ( less @ ( pl @ A @ z ) @ ( pl @ x @ z ) )
!= ( less @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38,24]) ).
thf(166,plain,
! [B: nat,A: nat] :
( ~ ( less @ A @ y )
| ( ( less @ ( pl @ A @ z ) @ ( pl @ x @ z ) )
!= ( less @ B @ B ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(167,plain,
~ ( less @ x @ y ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( x )),bind(B,$thf( pl @ x @ z ))]]) ).
thf(225,plain,
( ( more @ x @ y )
| $false ),
inference(rewrite,[status(thm)],[86,167]) ).
thf(226,plain,
more @ x @ y,
inference(simp,[status(thm)],[225]) ).
thf(8,axiom,
! [A: nat,B: nat,C: nat] :
( ( more @ A @ B )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(31,plain,
! [A: nat,B: nat,C: nat] :
( ( more @ A @ B )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,plain,
! [A: nat,B: nat] :
( ( more @ A @ B )
=> ! [C: nat] : ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(miniscope,[status(thm)],[31]) ).
thf(33,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(316,plain,
! [C: nat,B: nat,A: nat] :
( ~ $true
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) )
| ( ( more @ x @ y )
!= ( more @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[226,33]) ).
thf(317,plain,
! [C: nat,B: nat,A: nat] :
( ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) )
| ( ( more @ x @ y )
!= ( more @ A @ B ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
! [A: nat] : ( more @ ( pl @ x @ A ) @ ( pl @ y @ A ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(327,plain,
! [A: nat] : ( more @ ( pl @ x @ A ) @ ( pl @ y @ A ) ),
inference(simp,[status(thm)],[318]) ).
thf(329,plain,
! [A: nat] :
( ( more @ ( pl @ x @ A ) @ ( pl @ x @ z ) )
| ( ( pl @ y @ z )
!= ( pl @ y @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12,327]) ).
thf(330,plain,
more @ ( pl @ x @ z ) @ ( pl @ x @ z ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( z ))]]) ).
thf(17,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( more @ A @ B ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(20,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( more @ A @ B ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(21,plain,
! [A: nat] :
~ ( more @ A @ A ),
inference(simp,[status(thm)],[20]) ).
thf(372,plain,
$false,
inference(rewrite,[status(thm)],[330,21]) ).
thf(373,plain,
$false,
inference(simp,[status(thm)],[372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM681^1 : 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
% 0.09/0.20 % Computer : n009.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 12:37:45 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.79/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.79 % [INFO] Parsing done (99ms).
% 1.16/0.80 % [INFO] Running in sequential loop mode.
% 1.37/0.99 % [INFO] eprover registered as external prover.
% 1.37/1.00 % [INFO] Scanning for conjecture ...
% 1.66/1.03 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.66/1.05 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.66/1.07 % [INFO] Problem is higher-order (TPTP THF).
% 1.66/1.07 % [INFO] Type checking passed.
% 1.66/1.07 % [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 ...
% 5.64/2.42 % [INFO] Killing All external provers ...
% 5.64/2.43 % Time passed: 2076ms (effective reasoning time: 1620ms)
% 5.64/2.43 % 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)>
% 5.64/2.43 % Axioms used in derivation (5): satz10b, i, satz19c, satz10a, satz19a
% 5.64/2.43 % No. of inferences in proof: 47
% 5.64/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2076 ms resp. 1620 ms w/o parsing
% 5.64/2.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.64/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------