%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU498^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n019.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 08:28:17 AM UTC 2026
% Result : Theorem 3.89s 2.03s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 31 ( 15 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 90 ( 11 ~; 0 |; 18 &; 51 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 32 ( 10 ^; 22 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(refl_decl,type,
refl: ( $i > $i > $o ) > $o ).
thf(antisymm_decl,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(asymm_decl,type,
asymm: ( $i > $i > $o ) > $o ).
thf(trans_decl,type,
trans: ( $i > $i > $o ) > $o ).
thf(po_decl,type,
po: ( $i > $i > $o ) > $o ).
thf(so_decl,type,
so: ( $i > $i > $o ) > $o ).
thf(refl_def,definition,
( refl
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
thf(antisymm_def,definition,
( antisymm
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) ) ) ) ).
thf(asymm_def,definition,
( asymm
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) ) ) ).
thf(trans_def,definition,
( trans
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(po_def,definition,
( po
= ( ^ [A: $i > $i > $o] :
( ( refl @ A )
& ( antisymm @ A )
& ( trans @ A ) ) ) ) ).
thf(so_def,definition,
( so
= ( ^ [A: $i > $i > $o] :
( ( asymm @ A )
& ( trans @ A ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( ( po @ A )
=> ( so
@ ^ [B: $i,C: $i] :
( ( A @ B @ C )
& ( B != C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partial_order_induces_strict_order) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( ( po @ A )
=> ( so
@ ^ [B: $i,C: $i] :
( ( A @ B @ C )
& ( B != C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o] :
( ( ! [B: $i] : ( A @ B @ B )
& ! [B: $i,C: $i] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) )
=> ( ! [B: $i,C: $i] :
( ( ( A @ B @ C )
& ( B != C ) )
=> ~ ( ( A @ C @ B )
& ( C != B ) ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( B != C )
& ( A @ C @ D )
& ( C != D ) )
=> ( ( A @ B @ D )
& ( B != D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(25,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU498^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.21 % Computer : n019.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:46:32 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.70/0.57 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/0.80 % [INFO] Parsing done (236ms).
% 1.47/0.82 % [INFO] Running in sequential loop mode.
% 2.08/1.21 % [INFO] eprover registered as external prover.
% 2.08/1.22 % [INFO] Scanning for conjecture ...
% 2.26/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.50/1.42 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.50/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 2.50/1.42 % [INFO] Type checking passed.
% 2.50/1.43 % [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 ...
% 3.53/2.03 % External prover 'e' found a proof!
% 3.89/2.03 % [INFO] Killing All external provers ...
% 3.89/2.03 % Time passed: 1722ms (effective reasoning time: 1205ms)
% 3.89/2.03 % 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)>
% 3.89/2.03 % Axioms used in derivation (0):
% 3.89/2.03 % No. of inferences in proof: 4
% 3.89/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1722 ms resp. 1205 ms w/o parsing
% 3.89/2.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.89/2.08 % [INFO] Killing All external provers ...
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