%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO209^5 : 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 : n015.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 08:45:24 AM UTC 2026
% Result : Theorem 20.28s 7.72s
% Output : Refutation 20.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 16 unt; 0 typ; 2 def)
% Number of atoms : 113 ( 31 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 265 ( 49 ~; 24 |; 0 &; 186 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 84 ( 15 ^; 58 !; 9 ?; 84 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > a > $o ).
thf(sk2_decl,type,
sk2: ( a > $o ) > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > a > $o] :
! [B: a > $o] :
? [C: a] :
! [D: ( a > $o ) > $o] :
( ( D @ ( A @ C ) )
=> ( D @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: a > $o] :
@+[B: a] :
! [C: ( a > $o ) > $o] :
( ( C @ ( sk1 @ B ) )
=> ( C @ A ) ) ) ) ).
thf(1,conjecture,
~ ? [A: a > a > $o] :
! [B: a > $o] :
? [C: a] :
! [D: ( a > $o ) > $o] :
( ( D @ ( A @ C ) )
=> ( D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCT29) ).
thf(2,negated_conjecture,
~ ~ ? [A: a > a > $o] :
! [B: a > $o] :
? [C: a] :
! [D: ( a > $o ) > $o] :
( ( D @ ( A @ C ) )
=> ( D @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ~ ? [A: a > a > $o] :
! [B: a > $o] :
? [C: a] :
! [D: ( a > $o ) > $o] :
( ( D @ ( A @ C ) )
=> ( D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
? [A: a > a > $o] :
! [B: a > $o] :
? [C: a] :
! [D: ( a > $o ) > $o] :
( ( D @ ( A @ C ) )
=> ( D @ B ) ),
inference(polarity_switch,[status(thm)],[3]) ).
thf(5,plain,
! [B: ( a > $o ) > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ ( sk2 @ A ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [A: a > $o] :
( ( ( sk1 @ ( sk2 @ A ) )
!= ( sk1 @ ( sk2 @ A ) ) )
| ( ( sk1 @ ( sk2 @ A ) )
= A ) ),
inference(replace_leibeq,[status(thm)],[5:[bind(A,$thf( A )),bind(B,$thf( (=) @ ( a > $o ) @ ( sk1 @ ( sk2 @ A ) ) ))]]) ).
thf(7,plain,
! [A: a > $o] :
( ( ( sk1 @ ( sk2 @ A ) )
!= ( sk1 @ ( sk2 @ A ) ) )
| ( ( sk1 @ ( sk2 @ A ) )
= A ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(8,plain,
! [A: a > $o] :
( ( sk1 @ ( sk2 @ A ) )
= A ),
inference(simp,[status(thm)],[7]) ).
thf(9,plain,
! [B: a,A: a > $o] :
( ( sk1 @ ( sk2 @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(11,plain,
! [B: a,A: a > $o] :
( ( sk1 @ ( sk2 @ A ) @ B )
| ~ ( A @ B ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(544,plain,
! [A: a] :
( ( sk1
@ ( sk2
@ ^ [B: a] : $true )
@ A )
| ~ $true ),
inference(prim_subst,[status(thm)],[11:[bind(A,$thf( ^ [C: a] : $true ))]]) ).
thf(600,plain,
! [A: a] :
( sk1
@ ( sk2
@ ^ [B: a] : $true )
@ A ),
inference(simp,[status(thm)],[544]) ).
thf(10,plain,
! [B: a,A: a > $o] :
( ~ ( sk1 @ ( sk2 @ A ) @ B )
| ( A @ B ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(403,plain,
! [A: a] :
( ~ ( sk1
@ ( sk2
@ ^ [B: a] : $false )
@ A )
| $false ),
inference(prim_subst,[status(thm)],[10:[bind(A,$thf( ^ [C: a] : $false ))]]) ).
thf(448,plain,
! [A: a] :
~ ( sk1
@ ( sk2
@ ^ [B: a] : $false )
@ A ),
inference(simp,[status(thm)],[403]) ).
thf(620,plain,
! [B: a,A: a] :
( ~ $true
| ( ( sk1
@ ( sk2
@ ^ [C: a] : $true )
@ A )
!= ( sk1
@ ( sk2
@ ^ [C: a] : $false )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[600,448]) ).
thf(621,plain,
! [B: a,A: a] :
( ( sk1
@ ( sk2
@ ^ [C: a] : $true )
@ A )
!= ( sk1
@ ( sk2
@ ^ [C: a] : $false )
@ B ) ),
inference(simp,[status(thm)],[620]) ).
thf(682,plain,
! [B: a,A: a] :
( ( ( sk2
@ ^ [C: a] : $false )
!= ( sk2
@ ^ [C: a] : $true ) )
| ( A != B ) ),
inference(simp,[status(thm)],[621]) ).
thf(709,plain,
( ( sk2
@ ^ [A: a] : $false )
!= ( sk2
@ ^ [A: a] : $true ) ),
inference(simp,[status(thm)],[682]) ).
thf(16,plain,
! [C: ( a > $o ) > $o,B: a > $o,A: a > $o] :
( ~ ( C @ ( sk1 @ ( sk2 @ A ) ) )
| ( C @ B )
| ( A
!= ( sk1 @ ( sk2 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,5]) ).
thf(17,plain,
! [B: ( a > $o ) > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) ) )
| ( B @ A ) ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( sk1 @ ( sk2 @ B ) )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(29,plain,
! [A: a > $o] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) ) )
| ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) )
= A ) ),
inference(replace_leibeq,[status(thm)],[17:[bind(A,$thf( A )),bind(B,$thf( (=) @ ( a > $o ) @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) ) ))]]) ).
thf(31,plain,
! [A: a > $o] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) ) )
| ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) )
= A ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(42,plain,
! [A: a > $o] :
( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[31:[]]) ).
thf(56,plain,
! [A: a > $o] :
( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) )
= A ),
inference(simp,[status(thm)],[42]) ).
thf(75,plain,
! [B: a > $o,A: a > $o] :
( ( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) )
= B )
| ( A
!= ( sk1 @ ( sk2 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,8]) ).
thf(76,plain,
! [A: a > $o] :
( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) ) ) )
= A ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( sk1 @ ( sk2 @ B ) )),bind(B,$thf( B ))]]) ).
thf(97,plain,
! [A: a > $o] :
( ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ ( sk1 @ ( sk2 @ A ) ) ) ) ) )
= A ),
inference(simp,[status(thm)],[76]) ).
thf(24,plain,
! [B: ( a > $o ) > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ ( sk2 @ A ) ) )
| ( ( B @ A )
!= ( ~ ( B @ ( sk1 @ ( sk2 @ A ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[5]) ).
thf(47,plain,
! [B: ( a > $o ) > $o,A: a > $o] :
( ~ ( B @ ( sk1 @ ( sk2 @ A ) ) )
| ( ( B @ A )
!= ( ~ ( B @ ( sk1 @ ( sk2 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[24]) ).
thf(127,plain,
! [C: ( a > $o ) > $o,B: a > $o,A: a > $o] :
( ~ ( C @ A )
| ( ( C @ B )
!= ( ~ ( C @ ( sk1 @ ( sk2 @ B ) ) ) ) )
| ( ( sk1 @ ( sk2 @ A ) )
!= ( sk1 @ ( sk2 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,47]) ).
thf(128,plain,
! [B: ( a > $o ) > $o,A: a > $o] :
( ~ ( B @ A )
| ( ( B @ A )
!= ( ~ ( B @ ( sk1 @ ( sk2 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(166,plain,
! [B: ( a > $o ) > $o,A: a > $o] :
( ~ ( B @ A )
| ( ( B @ A )
!= ( ~ ( B @ ( sk1 @ ( sk2 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(401,plain,
! [B: a,A: a > $o] :
( ~ ( sk1 @ ( sk2 @ A ) @ B )
| ( ( A @ B )
!= ( ~ ( sk1 @ ( sk2 @ A ) @ B ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10]) ).
thf(432,plain,
~ ( sk1
@ ( sk2
@ ^ [A: a] :
~ ( sk1 @ A @ A ) )
@ ( sk2
@ ^ [A: a] :
~ ( sk1 @ A @ A ) ) ),
inference(pre_uni,[status(thm)],[401:[bind(A,$thf( ^ [C: a] : ~ ( sk1 @ C @ C ) )),bind(B,$thf( sk2 @ ^ [C: a] : ~ ( sk1 @ C @ C ) ))]]) ).
thf(793,plain,
$false,
inference(e,[status(thm)],[5,709,448,97,9,166,3,8,432,47,10,56,600,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO209^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.10/0.20 % Computer : n015.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
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:42:48 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.97 % [INFO] Parsing done (184ms).
% 1.25/0.98 % [INFO] Running in sequential loop mode.
% 1.87/1.38 % [INFO] eprover registered as external prover.
% 1.87/1.39 % [INFO] Scanning for conjecture ...
% 2.07/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.25/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.25/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.25/1.51 % [INFO] Type checking passed.
% 2.25/1.51 % [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 ...
% 20.28/7.71 % External prover 'e' found a proof!
% 20.28/7.71 % [INFO] Killing All external provers ...
% 20.28/7.72 % Time passed: 7371ms (effective reasoning time: 6729ms)
% 20.28/7.72 % 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)>
% 20.28/7.72 % Axioms used in derivation (0):
% 20.28/7.72 % No. of inferences in proof: 36
% 20.28/7.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7371 ms resp. 6729 ms w/o parsing
% 20.28/7.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.28/7.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------