%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV288^5 : TPTP v9.3.1. Released 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 : 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 08:37:07 AM UTC 2026
% Result : Theorem 7.47s 3.50s
% Output : Refutation 7.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 21 unt; 0 typ; 2 def)
% Number of atoms : 65 ( 40 equ; 4 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 147 ( 45 ~; 28 |; 2 &; 59 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 8 ^; 16 !; 0 ?; 26 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk5_decl,type,
sk5: a > $o ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
~ ( ( A @ sk1 )
=> ( A @ sk2 ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: a > $o] :
~ ( ( A @ sk1 )
=> ( A @ sk2 ) ) ) ) ).
thf(1,conjecture,
( ( ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
= ( (=) @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cE1_eq__pme) ).
thf(2,negated_conjecture,
( ( ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
!= ( (=) @ a ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
!= ( (=) @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: a,B: a] :
! [C: a > $o] :
( ( C @ A )
=> ( C @ B ) ) )
!= ( (=) @ a ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: a > $o] :
( ( A @ sk1 )
=> ( A @ sk2 ) ) )
!= ( sk1 = sk2 ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(7,plain,
( ! [A: a > $o] :
( ( A @ sk1 )
=> ( A @ sk2 ) )
| ( sk1 = sk2 ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( sk2 = sk1 )
| ! [A: a > $o] :
( ( A @ sk1 )
=> ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
! [A: a > $o] :
( ( sk2 = sk1 )
| ~ ( A @ sk1 )
| ( A @ sk2 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(6,plain,
( ~ ! [A: a > $o] :
( ( A @ sk1 )
=> ( A @ sk2 ) )
| ( sk1 != sk2 ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( sk2 != sk1 )
| ~ ! [A: a > $o] :
( ( A @ sk1 )
=> ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
( ( ( sk2 != sk1 )
| ( sk3 @ sk1 ) )
& ( ( sk2 != sk1 )
| ~ ( sk3 @ sk2 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
( ( sk2 != sk1 )
| ( sk3 @ sk1 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(12,plain,
( ( sk2 != sk1 )
| ~ ( sk3 @ sk2 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(14,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 )
| ~ $true
| ( ( sk3 @ sk2 )
!= ( sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[11,12]) ).
thf(15,plain,
( ( sk2 != sk1 )
| ( ( sk3 @ sk2 )
!= ( sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
( ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
sk2 != sk1,
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
! [A: a > $o] :
( ~ ( A @ sk1 )
| ( A @ sk2 ) ),
inference(simplifyReflect,[status(thm)],[13,17]) ).
thf(22,plain,
! [A: a > $o] :
( ~ ( A @ sk1 )
| ~ ! [B: a > $o] :
( ( B @ sk1 )
=> ( B @ sk2 ) )
| ( ( A @ sk2 )
!= ( sk1 = sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[18,5]) ).
thf(33,plain,
( ( sk1 != sk1 )
| ~ ! [A: a > $o] :
( ( A @ sk1 )
=> ( A @ sk2 ) ) ),
inference(pre_uni,[status(thm)],[22:[bind(A,$thf( (=) @ a @ sk1 ))]]) ).
thf(39,plain,
( ( ( sk1 != sk1 )
| ( sk5 @ sk1 ) )
& ( ( sk1 != sk1 )
| ~ ( sk5 @ sk2 ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(40,plain,
( ( sk1 != sk1 )
| ( sk5 @ sk1 ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(42,plain,
( ( sk1 != sk1 )
| ( sk5 @ sk1 ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(43,plain,
sk5 @ sk1,
inference(simp,[status(thm)],[42]) ).
thf(53,plain,
! [A: a > $o] :
( ~ $true
| ( A @ sk2 )
| ( ( sk5 @ sk1 )
!= ( A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[43,18]) ).
thf(54,plain,
! [A: a > $o] :
( ( A @ sk2 )
| ( ( sk5 @ sk1 )
!= ( A @ sk1 ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(56,plain,
sk5 @ sk2,
inference(pre_uni,[status(thm)],[54:[bind(A,$thf( sk5 ))]]) ).
thf(41,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ sk2 ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(44,plain,
( ( sk1 != sk1 )
| ~ ( sk5 @ sk2 ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(45,plain,
~ ( sk5 @ sk2 ),
inference(simp,[status(thm)],[44]) ).
thf(64,plain,
$false,
inference(rewrite,[status(thm)],[56,45]) ).
thf(65,plain,
$false,
inference(simp,[status(thm)],[64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV288^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.27/0.31 % Computer : n020.cluster.edu
% 0.27/0.31 % Model : x86_64 x86_64
% 0.27/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.31 % Memory : 8046.5625MB
% 0.27/0.31 % OS : Linux 6.8.0-71-generic
% 0.27/0.31 % CPULimit : 300
% 0.27/0.31 % WCLimit : 300
% 0.27/0.31 % DateTime : Tue Sep 29 15:32:04 UTC 2026
% 0.27/0.32 % CPUTime :
% 0.27/0.32 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
% 1.36/1.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.00/1.40 % [INFO] Parsing done (254ms).
% 2.00/1.42 % [INFO] Running in sequential loop mode.
% 2.72/2.02 % [INFO] eprover registered as external prover.
% 2.72/2.03 % [INFO] Scanning for conjecture ...
% 3.02/2.15 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.20/2.19 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.20/2.19 % [INFO] Problem is higher-order (TPTP THF).
% 3.27/2.20 % [INFO] Type checking passed.
% 3.27/2.21 % [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 ...
% 7.24/3.49 % [INFO] Killing All external provers ...
% 7.24/3.49 % Time passed: 2968ms (effective reasoning time: 2059ms)
% 7.24/3.49 % 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)>
% 7.24/3.50 % Axioms used in derivation (0):
% 7.24/3.50 % No. of inferences in proof: 32
% 7.47/3.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2968 ms resp. 2059 ms w/o parsing
% 7.47/3.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.47/3.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------