%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU548^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 : n007.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 08:28:29 AM UTC 2026
% Result : Theorem 2.50s 1.37s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 72 ( 40 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 96 ( 13 ~; 3 |; 3 &; 56 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 34 ( 0 ^; 30 !; 0 ?; 34 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(inCongP_decl,type,
inCongP: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(inCongP_def,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
=> ( in @ D @ B ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 = A )
=> ! [B: $i,C: $i] :
( ( B = C )
=> ( ( in @ B @ sk1 )
= ( in @ C @ A ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( A = B )
=> ( ( in @ A @ sk1 )
= ( in @ B @ sk2 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk3 = A )
=> ( ( in @ sk3 @ sk1 )
= ( in @ A @ sk2 ) ) ) ) ) ).
thf(1,conjecture,
( inCongP
=> ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(2,negated_conjecture,
~ ( inCongP
=> ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
=> ( in @ D @ B ) ) ) )
=> ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A != B )
| ( C != D )
| ~ ( in @ C @ A )
| ( in @ D @ B ) )
& ( sk1 = sk2 )
& ( sk3 = sk4 )
& ( ( in @ sk3 @ sk1 )
!= ( in @ sk4 @ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
( ( in @ sk3 @ sk1 )
!= ( in @ sk4 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(13,plain,
( ( in @ sk4 @ sk2 )
!= ( in @ sk3 @ sk1 ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(6,plain,
sk1 = sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
sk2 = sk1,
inference(lifteq,[status(thm)],[6]) ).
thf(7,plain,
sk3 = sk4,
inference(cnfConj,[status(thm)],[4]) ).
thf(12,plain,
sk4 = sk3,
inference(lifteq,[status(thm)],[7]) ).
thf(14,plain,
( ( in @ sk3 @ sk1 )
!= ( in @ sk3 @ sk1 ) ),
inference(rewrite,[status(thm)],[13,11,12]) ).
thf(15,plain,
$false,
inference(simp,[status(thm)],[14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU548^2 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.09 % 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
% 0.10/0.22 % Computer : n007.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:47:25 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 0.68/0.54 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.02/0.64 % [INFO] Parsing done (95ms).
% 1.02/0.65 % [INFO] Running in sequential loop mode.
% 1.32/0.84 % [INFO] eprover registered as external prover.
% 1.32/0.84 % [INFO] Scanning for conjecture ...
% 1.32/0.89 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.58/0.91 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.58/0.91 % [INFO] Problem is higher-order (TPTP THF).
% 1.58/0.91 % [INFO] Type checking passed.
% 1.58/0.92 % [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 ...
% 2.50/1.36 % [INFO] Killing All external provers ...
% 2.50/1.36 % Time passed: 1044ms (effective reasoning time: 710ms)
% 2.50/1.36 % 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)>
% 2.50/1.36 % Axioms used in derivation (0):
% 2.50/1.36 % No. of inferences in proof: 12
% 2.50/1.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1044 ms resp. 710 ms w/o parsing
% 2.77/1.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.77/1.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------