%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM783^1 : 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 : n020.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 08:18:10 AM UTC 2026
% Result : Theorem 3.35s 2.07s
% Output : Refutation 3.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 121 ( 9 ~; 0 |; 1 &; 108 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 14 ( 0 ^; 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
thf(rat_type,type,
rat: $tType ).
thf(x0_decl,type,
x0: rat ).
thf(y0_decl,type,
y0: rat ).
thf(or3_decl,type,
or3: $o > $o > $o > $o ).
thf(is_decl,type,
is: rat > rat > $o ).
thf(more_decl,type,
more: rat > rat > $o ).
thf(less_decl,type,
less: rat > rat > $o ).
thf(ec3_decl,type,
ec3: $o > $o > $o > $o ).
thf(1,conjecture,
or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81a) ).
thf(2,negated_conjecture,
~ ( or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( or3 @ ( is @ x0 @ y0 ) @ ( more @ x0 @ y0 ) @ ( less @ x0 @ y0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: rat,B: rat] :
~ ( ( or3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) )
=> ~ ( ec3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz81) ).
thf(7,plain,
! [A: rat,B: rat] :
~ ( ( or3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) )
=> ~ ( ec3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,plain,
~ ( ! [A: rat,B: rat] : ( or3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) )
=> ~ ! [A: rat,B: rat] : ( ec3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ) ),
inference(miniscope,[status(thm)],[7]) ).
thf(9,plain,
! [D: rat,C: rat,B: rat,A: rat] :
( ( or3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) )
& ( ec3 @ ( is @ C @ D ) @ ( more @ C @ D ) @ ( less @ C @ D ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
! [B: rat,A: rat] : ( or3 @ ( is @ A @ B ) @ ( more @ A @ B ) @ ( less @ A @ B ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(13,plain,
~ $true,
inference(rewrite,[status(thm)],[5,10]) ).
thf(14,plain,
$false,
inference(simp,[status(thm)],[13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM783^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % 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
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 12:56:19 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
% 0.88/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (190ms).
% 1.23/0.99 % [INFO] Running in sequential loop mode.
% 1.84/1.38 % [INFO] eprover registered as external prover.
% 1.84/1.39 % [INFO] Scanning for conjecture ...
% 2.03/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.21/1.51 % [INFO] Axiom selection finished. Selected 2 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 ...
% 3.35/2.07 % [INFO] Killing All external provers ...
% 3.35/2.07 % Time passed: 1734ms (effective reasoning time: 1075ms)
% 3.35/2.07 % 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)>
% 3.35/2.07 % Axioms used in derivation (1): satz81
% 3.35/2.07 % No. of inferences in proof: 10
% 3.35/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1734 ms resp. 1075 ms w/o parsing
% 3.35/2.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.35/2.11 % [INFO] Killing All external provers ...
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