%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP006^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 08:06:17 AM UTC 2026
% Result : Theorem 4.65s 2.55s
% Output : Refutation 4.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 58 ( 19 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 209 ( 16 ~; 1 |; 12 &; 154 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 1 con; 0-4 aty)
% Number of variables : 72 ( 0 ^; 61 !; 8 ?; 72 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(skt2_type,type,
skt2: $tType ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS_decl,type,
c_2EquantHeuristics_2EGUESS__EXISTS:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_decl,type,
c_2EquantHeuristics_2EGUESS__EXISTS__GAP:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_decl,type,
c_2EquantHeuristics_2EGUESS__EXISTS__POINT:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__FORALL_decl,type,
c_2EquantHeuristics_2EGUESS__FORALL:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__FORALL__GAP_decl,type,
c_2EquantHeuristics_2EGUESS__FORALL__GAP:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > $o ) > $o ) ).
thf(c_2EquantHeuristics_2EGUESS__FORALL__POINT_decl,type,
c_2EquantHeuristics_2EGUESS__FORALL__POINT:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > ( TA > $o ) > $o ) ).
thf(sk1_decl,type,
sk1: skt2 > skt1 ).
thf(sk2_decl,type,
sk2: skt1 > $o ).
thf(sk3_decl,type,
sk3: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt2 > skt1] :
~ ! [B: skt1 > $o,C: skt1 > $o] :
( ! [D: skt1] :
( ( C @ D )
=> ( B @ D ) )
=> ( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ A @ B )
=> ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ A @ C ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: skt1 > $o] :
~ ! [B: skt1 > $o] :
( ! [C: skt1] :
( ( B @ C )
=> ( A @ C ) )
=> ( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ A )
=> ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ B ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: skt1 > $o] :
~ ( ! [B: skt1] :
( ( A @ B )
=> ( sk2 @ B ) )
=> ( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ sk2 )
=> ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ A ) ) ) ) ) ).
thf(1,conjecture,
! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o,C: TB > $o] :
( ! [D: TB] :
( ( C @ D )
=> ( B @ D ) )
=> ( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TA @ TB @ A @ B )
=> ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TA @ TB @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o,C: TB > $o] :
( ! [D: TB] :
( ( C @ D )
=> ( B @ D ) )
=> ( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TA @ TB @ A @ B )
=> ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TA @ TB @ A @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [TA: $tType,TB: $tType,A: TA > TB,B: TB > $o,C: TB > $o] :
( ! [D: TB] :
( ( C @ D )
=> ( B @ D ) )
=> ( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TA @ TB @ A @ B )
=> ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TA @ TB @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > $o] :
( ( ( c_2EquantHeuristics_2EGUESS__EXISTS @ TB @ TA @ A @ B )
= ( ! [C: TA] :
( ( B @ C )
=> ? [D: TB] : ( B @ ( A @ D ) ) ) ) )
& ( ( c_2EquantHeuristics_2EGUESS__FORALL @ TB @ TA @ A @ B )
= ( ! [C: TA] :
( ~ ( B @ C )
=> ? [D: TB] :
~ ( B @ ( A @ D ) ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ TB @ TA @ C @ D )
= ( ! [E: TB] : ( D @ ( C @ E ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TB @ TA @ C @ D )
= ( ! [E: TB] :
~ ( D @ ( C @ E ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ TB @ TA @ C @ D )
= ( ! [E: TA] :
( ( D @ E )
=> ? [F: TB] :
( E
= ( C @ F ) ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ TB @ TA @ C @ D )
= ( ! [E: TA] :
( ~ ( D @ E )
=> ? [F: TB] :
( E
= ( C @ F ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2EquantHeuristics_2EGUESS__REWRITES) ).
thf(9,plain,
! [TA: $tType,TB: $tType,A: TB > TA,B: TA > $o] :
( ( ( c_2EquantHeuristics_2EGUESS__EXISTS @ TB @ TA @ A @ B )
= ( ! [C: TA] :
( ( B @ C )
=> ? [D: TB] : ( B @ ( A @ D ) ) ) ) )
& ( ( c_2EquantHeuristics_2EGUESS__FORALL @ TB @ TA @ A @ B )
= ( ! [C: TA] :
( ~ ( B @ C )
=> ? [D: TB] :
~ ( B @ ( A @ D ) ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__EXISTS__POINT @ TB @ TA @ C @ D )
= ( ! [E: TB] : ( D @ ( C @ E ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ TB @ TA @ C @ D )
= ( ! [E: TB] :
~ ( D @ ( C @ E ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__EXISTS__GAP @ TB @ TA @ C @ D )
= ( ! [E: TA] :
( ( D @ E )
=> ? [F: TB] :
( E
= ( C @ F ) ) ) ) )
& ! [C: TB > TA,D: TA > $o] :
( ( c_2EquantHeuristics_2EGUESS__FORALL__GAP @ TB @ TA @ C @ D )
= ( ! [E: TA] :
( ~ ( D @ E )
=> ? [F: TB] :
( E
= ( C @ F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,plain,
! [A: skt1] :
( ( ~ ( sk3 @ A )
| ( sk2 @ A ) )
& ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ sk2 )
& ~ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ sk3 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ sk2,
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
~ ( c_2EquantHeuristics_2EGUESS__FORALL__POINT @ skt2 @ skt1 @ sk1 @ sk3 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(43,plain,
$false,
inference(e,[status(thm)],[4,9,7,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP006^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.10/0.22 % Computer : n017.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 19:18:12 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.03/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.50/1.05 % [INFO] Parsing done (241ms).
% 1.50/1.07 % [INFO] Running in sequential loop mode.
% 2.20/1.47 % [INFO] eprover registered as external prover.
% 2.20/1.48 % [INFO] Scanning for conjecture ...
% 2.40/1.59 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 2.57/1.65 % [INFO] Axiom selection finished. Selected 1 axioms (removed 25 axioms).
% 2.57/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.57/1.69 % [INFO] Type checking passed.
% 2.57/1.69 % [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 ...
% 4.65/2.55 % External prover 'e' found a proof!
% 4.65/2.55 % [INFO] Killing All external provers ...
% 4.65/2.55 % Time passed: 2178ms (effective reasoning time: 1473ms)
% 4.65/2.55 % 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)>
% 4.65/2.55 % Axioms used in derivation (1): thm_2EquantHeuristics_2EGUESS__REWRITES
% 4.65/2.55 % No. of inferences in proof: 9
% 4.65/2.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2178 ms resp. 1473 ms w/o parsing
% 4.99/2.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.99/2.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------