%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO268^5 : 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 : n003.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 08:45:30 AM UTC 2026
% Result : Theorem 6.65s 2.97s
% Output : Refutation 7.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 5 def)
% Number of atoms : 92 ( 24 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 332 ( 44 ~; 30 |; 1 &; 250 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 99 ( 6 ^; 64 !; 24 ?; 99 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(r_decl,type,
r: a > b > $o ).
thf(sk1_decl,type,
sk1: ( b > $o ) > b ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: ( a > b ) > b > a ).
thf(sk4_decl,type,
sk4: a > b ).
thf(sk5_decl,type,
sk5: a > a > b ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( b > $o ) > b] :
! [B: b > $o] :
( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
~ ? [B: b] : ( r @ A @ B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: a > b,B: b] :
@+[C: a] :
~ ( r @ C @ ( A @ C ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: a] :
@+[B: b] : ( r @ A @ B ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: a] :
@+[B: a > b] :
! [C: a] : ( r @ C @ ( B @ C ) ) ) ) ).
thf(1,conjecture,
( ? [A: ( b > $o ) > b] :
! [B: b > $o] :
( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) )
=> ( ( ! [A: a] :
? [B: b] : ( r @ A @ B ) )
= ( ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5308) ).
thf(2,negated_conjecture,
~ ( ? [A: ( b > $o ) > b] :
! [B: b > $o] :
( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) )
=> ( ( ! [A: a] :
? [B: b] : ( r @ A @ B ) )
= ( ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ? [A: ( b > $o ) > b] :
! [B: b > $o] :
( ? [C: b] : ( B @ C )
=> ( B @ ( A @ B ) ) )
=> ( ( ! [A: a] :
? [B: b] : ( r @ A @ B ) )
= ( ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: b,A: b > $o] :
( ( ~ ( A @ B )
| ( A @ ( sk1 @ A ) ) )
& ( ( ! [C: a] :
? [D: b] : ( r @ C @ D ) )
!= ( ? [C: a > b] :
! [D: a] : ( r @ D @ ( C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
( ( ! [A: a] :
? [B: b] : ( r @ A @ B ) )
!= ( ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ( ! [A: a] :
? [B: b] : ( r @ A @ B ) )
!= ( ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(8,plain,
( ~ ! [A: a] :
? [B: b] : ( r @ A @ B )
| ~ ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(10,plain,
! [B: a > b,A: b] :
( ~ ( r @ sk2 @ A )
| ~ ( r @ ( sk3 @ B @ A ) @ ( B @ ( sk3 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(26,plain,
! [B: a > b,A: b] :
( ~ ( r @ sk2 @ A )
| ( ( r @ ( sk3 @ B @ A ) @ ( B @ ( sk3 @ B @ A ) ) )
!= ( r @ sk2 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[10]) ).
thf(29,plain,
! [B: a > b,A: b] :
( ~ ( r @ sk2 @ A )
| ( ( r @ ( sk3 @ B @ A ) @ ( B @ ( sk3 @ B @ A ) ) )
!= ( r @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(9,plain,
( ! [A: a] :
? [B: b] : ( r @ A @ B )
| ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(11,plain,
! [B: a,A: a] :
( ( r @ A @ ( sk4 @ A ) )
| ( r @ B @ ( sk5 @ A @ B ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(19,plain,
! [D: a > b,C: b,B: a,A: a] :
( ( r @ B @ ( sk5 @ A @ B ) )
| ~ ( r @ sk2 @ C )
| ~ $true
| ( ( r @ A @ ( sk4 @ A ) )
!= ( r @ ( sk3 @ D @ C ) @ ( D @ ( sk3 @ D @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(20,plain,
! [D: a > b,C: b,B: a,A: a] :
( ( r @ B @ ( sk5 @ A @ B ) )
| ~ ( r @ sk2 @ C )
| ( ( r @ A @ ( sk4 @ A ) )
!= ( r @ ( sk3 @ D @ C ) @ ( D @ ( sk3 @ D @ C ) ) ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(28,plain,
! [B: b,A: a] :
( ( r @ A @ ( sk5 @ ( sk3 @ sk4 @ B ) @ A ) )
| ~ ( r @ sk2 @ B ) ),
inference(pre_uni,[status(thm)],[20:[bind(A,$thf( sk3 @ sk4 @ C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk4 ))]]) ).
thf(34,plain,
! [B: b,A: a] :
( ( r @ A @ ( sk5 @ ( sk3 @ sk4 @ B ) @ A ) )
| ~ ( r @ sk2 @ B ) ),
inference(simp,[status(thm)],[28]) ).
thf(68,plain,
! [D: a > b,C: b,B: b,A: a] :
( ~ ( r @ sk2 @ B )
| ~ ( r @ sk2 @ C )
| ~ ( r @ sk2 @ C )
| ( ( r @ A @ ( sk5 @ ( sk3 @ sk4 @ B ) @ A ) )
!= ( r @ ( sk3 @ D @ C ) @ ( D @ ( sk3 @ D @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,29]) ).
thf(69,plain,
! [D: a > b,C: b,B: b,A: a] :
( ~ ( r @ sk2 @ B )
| ~ ( r @ sk2 @ C )
| ( ( r @ A @ ( sk5 @ ( sk3 @ sk4 @ B ) @ A ) )
!= ( r @ ( sk3 @ D @ C ) @ ( D @ ( sk3 @ D @ C ) ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(82,plain,
! [B: a > b,A: b] :
( ~ ( r @ sk2
@ ( B
@ ( sk3
@ ^ [C: a] : ( sk5 @ ( sk3 @ sk4 @ ( B @ C ) ) @ C )
@ A ) ) )
| ~ ( r @ sk2 @ A ) ),
inference(pre_uni,[status(thm)],[69:[bind(A,$thf( sk3 @ ^ [F: a] : ( sk5 @ ( sk3 @ sk4 @ ( L @ F ) ) @ F ) @ C )),bind(B,$thf( L @ ( sk3 @ ^ [F: a] : ( sk5 @ ( sk3 @ sk4 @ ( L @ F ) ) @ F ) @ C ) )),bind(C,$thf( C )),bind(D,$thf( ^ [F: a] : ( sk5 @ ( sk3 @ sk4 @ ( L @ F ) ) @ F ) ))]]) ).
thf(85,plain,
! [B: a > b,A: b] :
( ~ ( r @ sk2
@ ( B
@ ( sk3
@ ^ [C: a] : ( sk5 @ ( sk3 @ sk4 @ ( B @ C ) ) @ C )
@ A ) ) )
| ~ ( r @ sk2 @ A ) ),
inference(simp,[status(thm)],[82]) ).
thf(12,plain,
! [B: a,A: a] :
( ( r @ A @ ( sk4 @ A ) )
| ( ( r @ B @ ( sk5 @ A @ B ) )
!= ( r @ A @ ( sk4 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[11]) ).
thf(13,plain,
! [B: a,A: a] :
( ( r @ A @ ( sk4 @ A ) )
| ( ( r @ B @ ( sk5 @ A @ B ) )
!= ( r @ A @ ( sk4 @ A ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(30,plain,
! [B: a > b,A: b] :
( ~ ( r @ sk2 @ A )
| ( ( sk3 @ B @ A )
!= sk2 )
| ( ( B @ ( sk3 @ B @ A ) )
!= A ) ),
inference(simp,[status(thm)],[26]) ).
thf(14,plain,
! [B: a,A: a] :
( ( r @ A @ ( sk4 @ A ) )
| ( B != A )
| ( ( sk5 @ A @ B )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(15,plain,
! [A: a] :
( ( r @ A @ ( sk4 @ A ) )
| ( ( sk5 @ A @ A )
!= ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(188,plain,
$false,
inference(e,[status(thm)],[10,29,85,13,34,7,3,11,30,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO268^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:44:13 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.91/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.96 % [INFO] Parsing done (189ms).
% 1.24/0.98 % [INFO] Running in sequential loop mode.
% 1.80/1.37 % [INFO] eprover registered as external prover.
% 1.80/1.38 % [INFO] Scanning for conjecture ...
% 2.00/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.16/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.16/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.51 % [INFO] Type checking passed.
% 2.16/1.51 % [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 ...
% 6.65/2.96 % External prover 'e' found a proof!
% 6.65/2.96 % [INFO] Killing All external provers ...
% 6.65/2.96 % Time passed: 2627ms (effective reasoning time: 1980ms)
% 6.65/2.96 % 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)>
% 6.65/2.97 % Axioms used in derivation (0):
% 6.65/2.97 % No. of inferences in proof: 26
% 6.65/2.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2627 ms resp. 1980 ms w/o parsing
% 7.25/3.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.25/3.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------