%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO035^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:45:03 AM UTC 2026
% Result : Theorem 4.60s 2.78s
% Output : Refutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 13 unt; 0 typ; 5 def)
% Number of atoms : 62 ( 45 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 78 ( 17 ~; 7 |; 2 &; 38 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 51 ( 28 ^; 20 !; 0 ?; 51 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leibeq1_decl,type,
leibeq1: $i > $i > $o ).
thf(leibeq2_decl,type,
leibeq2: ( $i > $o ) > ( $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(leibeq1_def,definition,
( leibeq1
= ( ^ [A: $i,B: $i] :
! [C: $i > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(leibeq2_def,definition,
( leibeq2
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: ( $i > $o ) > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ! [C: ( $i > $o ) > $o] :
( ( C
@ ^ [D: $i] : ( D = A ) )
=> ( C
@ ^ [D: $i] : ( D = B ) ) )
=> ! [C: $i > $o] :
( ( C @ A )
=> ( C @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ! [B: ( $i > $o ) > $o] :
( ( B
@ ^ [C: $i] : ( C = sk1 ) )
=> ( B
@ ^ [C: $i] : ( C = A ) ) )
=> ! [B: $i > $o] :
( ( B @ sk1 )
=> ( B @ A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
~ ( ( A @ sk1 )
=> ( A @ sk2 ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( leibeq2
@ ^ [C: $i] : ( C = A )
@ ^ [C: $i] : ( C = B ) )
=> ( leibeq1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( leibeq2
@ ^ [C: $i] : ( C = A )
@ ^ [C: $i] : ( C = B ) )
=> ( leibeq1 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ! [C: ( $i > $o ) > $o] :
( ( C
@ ^ [D: $i] : ( D = A ) )
=> ( C
@ ^ [D: $i] : ( D = B ) ) )
=> ! [C: $i > $o] :
( ( C @ A )
=> ( C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $o ) > $o] :
( ( ~ ( A
@ ^ [B: $i] : ( B = sk1 ) )
| ( A
@ ^ [B: $i] : ( B = sk2 ) ) )
& ( sk3 @ sk1 )
& ~ ( sk3 @ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : ( B = sk1 ) )
| ( A
@ ^ [B: $i] : ( B = sk2 ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( ( ^ [A: $i] : ( A = sk1 ) )
!= ( ^ [A: $i] : ( A = sk1 ) ) )
| ( ( ^ [A: $i] : ( A = sk1 ) )
= ( ^ [A: $i] : ( A = sk2 ) ) ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) @ ^ [B: $i] : ( B = sk1 ) ))]]) ).
thf(9,plain,
( ( ( ^ [A: $i] : ( A = sk1 ) )
!= ( ^ [A: $i] : ( A = sk1 ) ) )
| ( ( ^ [A: $i] : ( A = sk2 ) )
= ( ^ [A: $i] : ( A = sk1 ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
( ( ^ [A: $i] : ( A = sk2 ) )
= ( ^ [A: $i] : ( A = sk1 ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(14,plain,
! [A: $i] :
( ( A = sk2 )
= ( A = sk1 ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(18,plain,
! [A: $i] :
( ( A != sk2 )
| ( A = sk1 ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(20,plain,
! [A: $i] :
( ( A != sk2 )
| ( A = sk1 ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(22,plain,
sk2 = sk1,
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( sk2 ))]]) ).
thf(6,plain,
sk3 @ sk1,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk3 @ sk2 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ~ $true
| ( ( sk3 @ sk2 )
!= ( sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(12,plain,
( ( sk3 @ sk2 )
!= ( sk3 @ sk1 ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
sk2 != sk1,
inference(simp,[status(thm)],[12]) ).
thf(24,plain,
$false,
inference(simplifyReflect,[status(thm)],[22,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO035^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:18:52 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.14/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.13 % [INFO] Parsing done (216ms).
% 1.57/1.15 % [INFO] Running in sequential loop mode.
% 2.27/1.61 % [INFO] eprover registered as external prover.
% 2.27/1.62 % [INFO] Scanning for conjecture ...
% 2.46/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.46/1.77 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.46/1.77 % [INFO] Problem is higher-order (TPTP THF).
% 2.46/1.78 % [INFO] Type checking passed.
% 2.46/1.79 % [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 ...
% 4.60/2.77 % [INFO] Killing All external provers ...
% 4.60/2.77 % Time passed: 2425ms (effective reasoning time: 1614ms)
% 4.60/2.77 % 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)>
% 4.60/2.77 % Axioms used in derivation (0):
% 4.60/2.77 % No. of inferences in proof: 18
% 4.60/2.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2425 ms resp. 1614 ms w/o parsing
% 4.90/2.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.90/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------