%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM789^1 : 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 : 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 08:18:11 AM UTC 2026
% Result : Theorem 4.51s 2.68s
% Output : Refutation 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 69 ( 4 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 209 ( 53 ~; 15 |; 2 &; 120 @)
% ( 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 : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(rat_type,type,
rat: $tType ).
thf(x0_decl,type,
x0: rat ).
thf(y0_decl,type,
y0: rat ).
thf(less_decl,type,
less: rat > rat > $o ).
thf(more_decl,type,
more: rat > rat > $o ).
thf(is_decl,type,
is: rat > rat > $o ).
thf(1,conjecture,
~ ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81h) ).
thf(2,negated_conjecture,
~ ~ ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ~ ( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( more @ x0 @ y0 )
| ( is @ x0 @ y0 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(3,axiom,
less @ x0 @ y0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(9,plain,
less @ x0 @ y0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: rat,B: rat] :
~ ( ( ( is @ A @ B )
=> ~ ( more @ A @ B ) )
=> ~ ~ ( ( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ( ( less @ A @ B )
=> ~ ( is @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81b) ).
thf(11,plain,
! [A: rat,B: rat] :
~ ( ( ( is @ A @ B )
=> ~ ( more @ A @ B ) )
=> ( ( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ( ( less @ A @ B )
=> ~ ( is @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,plain,
~ ( ! [A: rat,B: rat] :
( ( is @ A @ B )
=> ~ ( more @ A @ B ) )
=> ( ! [A: rat,B: rat] :
( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ! [A: rat,B: rat] :
( ( less @ A @ B )
=> ~ ( is @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[11]) ).
thf(13,plain,
! [F: rat,E: rat,D: rat,C: rat,B: rat,A: rat] :
( ( ~ ( is @ A @ B )
| ~ ( more @ A @ B ) )
& ( ~ ( more @ C @ D )
| ~ ( less @ C @ D ) )
& ( ~ ( less @ E @ F )
| ~ ( is @ E @ F ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(15,plain,
! [B: rat,A: rat] :
( ~ ( more @ A @ B )
| ~ ( less @ A @ B ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(17,plain,
! [B: rat,A: rat] :
( ~ ( more @ A @ B )
| ~ ( less @ A @ B ) ),
inference(simp,[status(thm)],[15]) ).
thf(22,plain,
! [B: rat,A: rat] :
( ~ ( more @ A @ B )
| ~ $true
| ( ( less @ x0 @ y0 )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,17]) ).
thf(23,plain,
! [B: rat,A: rat] :
( ~ ( more @ A @ B )
| ( ( less @ x0 @ y0 )
!= ( less @ A @ B ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
~ ( more @ x0 @ y0 ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( x0 )),bind(B,$thf( y0 ))]]) ).
thf(25,plain,
( $false
| ( is @ x0 @ y0 ) ),
inference(rewrite,[status(thm)],[8,24]) ).
thf(26,plain,
is @ x0 @ y0,
inference(simp,[status(thm)],[25]) ).
thf(16,plain,
! [B: rat,A: rat] :
( ~ ( less @ A @ B )
| ~ ( is @ A @ B ) ),
inference(cnfConj,[status(thm)],[13]) ).
thf(18,plain,
! [B: rat,A: rat] :
( ~ ( less @ A @ B )
| ~ ( is @ A @ B ) ),
inference(simp,[status(thm)],[16]) ).
thf(33,plain,
! [B: rat,A: rat] :
( ~ ( less @ A @ B )
| ~ $true
| ( ( is @ x0 @ y0 )
!= ( is @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26,18]) ).
thf(34,plain,
! [B: rat,A: rat] :
( ~ ( less @ A @ B )
| ( ( is @ x0 @ y0 )
!= ( is @ A @ B ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(35,plain,
~ ( less @ x0 @ y0 ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( x0 )),bind(B,$thf( y0 ))]]) ).
thf(36,plain,
~ $true,
inference(rewrite,[status(thm)],[35,9]) ).
thf(37,plain,
$false,
inference(simp,[status(thm)],[36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM789^1 : 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 : n011.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 12:56:16 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
% 0.87/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.95 % [INFO] Parsing done (178ms).
% 1.22/0.97 % [INFO] Running in sequential loop mode.
% 2.17/1.51 % [INFO] eprover registered as external prover.
% 2.17/1.52 % [INFO] Scanning for conjecture ...
% 2.33/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.33/1.67 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.46/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.46/1.71 % [INFO] Type checking passed.
% 2.46/1.72 % [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 ...
% 4.51/2.67 % [INFO] Killing All external provers ...
% 4.51/2.68 % Time passed: 2332ms (effective reasoning time: 1702ms)
% 4.51/2.68 % 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)>
% 4.51/2.68 % Axioms used in derivation (2): l, satz81b
% 4.51/2.68 % No. of inferences in proof: 25
% 4.51/2.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2332 ms resp. 1702 ms w/o parsing
% 4.76/2.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.76/2.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------