%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP004^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 08:06:16 AM UTC 2026
% Result : Theorem 7.05s 3.24s
% Output : Refutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 31 unt; 0 typ; 1 def)
% Number of atoms : 144 ( 34 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 170 ( 14 ~; 5 |; 8 &; 139 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 2 con; 0-4 aty)
% Number of variables : 59 ( 0 ^; 56 !; 2 ?; 59 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(c_2Ebool_2E_21_decl,type,
c_2Ebool_2E_21:
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(c_2Ebool_2E_2F_5C_decl,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Emin_2E_3D_decl,type,
c_2Emin_2E_3D:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(c_2Emin_2E_3D_3D_3E_decl,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F_decl,type,
c_2Ebool_2E_3F:
!>[TA: $tType] : ( ( TA > $o ) > $o ) ).
thf(c_2Epred__set_2ECHOICE_decl,type,
c_2Epred__set_2ECHOICE:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(c_2Epred__set_2EDELETE_decl,type,
c_2Epred__set_2EDELETE:
!>[TA: $tType] : ( ( TA > $o ) > TA > TA > $o ) ).
thf(c_2Ebool_2EIN_decl,type,
c_2Ebool_2EIN:
!>[TA: $tType] : ( TA > ( TA > $o ) > $o ) ).
thf(c_2Epred__set_2EREST_decl,type,
c_2Epred__set_2EREST:
!>[TA: $tType] : ( ( TA > $o ) > TA > $o ) ).
thf(c_2Epred__set_2ESUBSET_decl,type,
c_2Epred__set_2ESUBSET:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > $o ) ).
thf(c_2Ebool_2E_5C_2F_decl,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebool_2E_7E_decl,type,
c_2Ebool_2E_7E: $o > $o ).
thf(sk1_decl,type,
sk1: skt1 > $o ).
thf(sk1_def,definition,
( sk1
= ( @+[A: skt1 > $o] :
~ ( c_2Epred__set_2ESUBSET @ skt1 @ ( c_2Epred__set_2EREST @ skt1 @ A ) @ A ) ) ) ).
thf(10,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).
thf(56,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ( c_2Epred__set_2ESUBSET @ TA @ A @ B )
= ( ! [C: TA] :
( ( c_2Ebool_2EIN @ TA @ C @ A )
=> ( c_2Ebool_2EIN @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EREST @ TA @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EREST @ TA @ A ) @ A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [TA: $tType,A: TA > $o] : ( c_2Epred__set_2ESUBSET @ TA @ ( c_2Epred__set_2EREST @ TA @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
~ ( c_2Epred__set_2ESUBSET @ skt1 @ ( c_2Epred__set_2EREST @ skt1 @ sk1 ) @ sk1 ),
inference(cnf,[status(esa)],[13]) ).
thf(9,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_3F @ TA @ A )
= ( ? [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_3F) ).
thf(53,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_3F @ TA @ A )
= ( ? [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_2F_5C) ).
thf(15,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,plain,
( ( c_2Ebool_2E_2F_5C @ $true @ $true )
= ( $true
& $true ) ),
inference(instance,[status(thm)],[15]) ).
thf(17,plain,
c_2Ebool_2E_2F_5C @ $true @ $true,
inference(simp,[status(thm)],[16]) ).
thf(11,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) )
= ( ( c_2Ebool_2EIN @ TA @ B @ A )
& ( B != C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).
thf(59,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA] :
( ( c_2Ebool_2EIN @ TA @ B @ ( c_2Epred__set_2EDELETE @ TA @ A @ C ) )
= ( ( c_2Ebool_2EIN @ TA @ B @ A )
& ( B != C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ( ~ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(33,plain,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ( ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,plain,
( ( c_2Ebool_2E_7E @ $true )
= ( ~ $true ) ),
inference(instance,[status(thm)],[33]) ).
thf(35,plain,
~ ( c_2Ebool_2E_7E @ $true ),
inference(simp,[status(thm)],[34]) ).
thf(8,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_21 @ TA @ A )
= ( ! [B: TA] : ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantdef_2E_21) ).
thf(50,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Ebool_2E_21 @ TA @ A )
= ( ! [B: TA] : ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_5C_2F @ A @ B )
= ( A
| B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_5C_2F) ).
thf(24,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_5C_2F @ A @ B )
= ( A
| B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,plain,
( ( c_2Ebool_2E_7E @ $false )
= ( ~ $false ) ),
inference(instance,[status(thm)],[33]) ).
thf(37,plain,
c_2Ebool_2E_7E @ $false,
inference(simp,[status(thm)],[36]) ).
thf(20,plain,
( ( c_2Ebool_2E_2F_5C @ $false @ $true )
= ( $false
& $true ) ),
inference(instance,[status(thm)],[15]) ).
thf(21,plain,
~ ( c_2Ebool_2E_2F_5C @ $false @ $true ),
inference(simp,[status(thm)],[20]) ).
thf(27,plain,
( ( c_2Ebool_2E_5C_2F @ $true @ $false )
= ( $true
| $false ) ),
inference(instance,[status(thm)],[24]) ).
thf(28,plain,
c_2Ebool_2E_5C_2F @ $true @ $false,
inference(simp,[status(thm)],[27]) ).
thf(6,axiom,
! [A: $o,B: $o] :
( ( c_2Emin_2E_3D_3D_3E @ A @ B )
= ( A
=> B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D_3D_3E) ).
thf(38,plain,
! [A: $o,B: $o] :
( ( c_2Emin_2E_3D_3D_3E @ A @ B )
= ( A
=> B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,plain,
( ( c_2Ebool_2E_5C_2F @ $true @ $true )
= ( $true
| $true ) ),
inference(instance,[status(thm)],[24]) ).
thf(26,plain,
c_2Ebool_2E_5C_2F @ $true @ $true,
inference(simp,[status(thm)],[25]) ).
thf(22,plain,
( ( c_2Ebool_2E_2F_5C @ $false @ $false )
= ( $false
& $false ) ),
inference(instance,[status(thm)],[15]) ).
thf(23,plain,
~ ( c_2Ebool_2E_2F_5C @ $false @ $false ),
inference(simp,[status(thm)],[22]) ).
thf(29,plain,
( ( c_2Ebool_2E_5C_2F @ $false @ $true )
= ( $false
| $true ) ),
inference(instance,[status(thm)],[24]) ).
thf(30,plain,
c_2Ebool_2E_5C_2F @ $false @ $true,
inference(simp,[status(thm)],[29]) ).
thf(18,plain,
( ( c_2Ebool_2E_2F_5C @ $true @ $false )
= ( $true
& $false ) ),
inference(instance,[status(thm)],[15]) ).
thf(19,plain,
~ ( c_2Ebool_2E_2F_5C @ $true @ $false ),
inference(simp,[status(thm)],[18]) ).
thf(7,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Emin_2E_3D @ TA @ A @ B )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_3D) ).
thf(47,plain,
! [TA: $tType,A: TA,B: TA] :
( ( c_2Emin_2E_3D @ TA @ A @ B )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EREST @ TA @ A )
= ( c_2Epred__set_2EDELETE @ TA @ A @ ( c_2Epred__set_2ECHOICE @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).
thf(62,plain,
! [TA: $tType,A: TA > $o] :
( ( c_2Epred__set_2EREST @ TA @ A )
= ( c_2Epred__set_2EDELETE @ TA @ A @ ( c_2Epred__set_2ECHOICE @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(108,plain,
$false,
inference(e,[status(thm)],[56,14,53,13,17,59,35,50,24,37,21,33,28,38,26,23,30,19,47,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP004^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.13 % 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
% 0.27/0.33 % Computer : n015.cluster.edu
% 0.27/0.33 % Model : x86_64 x86_64
% 0.27/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.33 % Memory : 8046.5625MB
% 0.27/0.33 % OS : Linux 6.8.0-71-generic
% 0.27/0.33 % CPULimit : 300
% 0.27/0.33 % WCLimit : 300
% 0.27/0.33 % DateTime : Tue Sep 29 19:23:48 UTC 2026
% 0.27/0.33 % CPUTime :
% 0.27/0.33 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
% 1.16/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.00 % [INFO] Parsing done (179ms).
% 1.38/1.02 % [INFO] Running in sequential loop mode.
% 2.39/1.48 % [INFO] eprover registered as external prover.
% 2.39/1.49 % [INFO] Scanning for conjecture ...
% 2.75/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.75/1.67 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.93/1.71 % [INFO] Problem is higher-order (TPTP THF).
% 2.93/1.72 % [INFO] Type checking passed.
% 2.93/1.73 % [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 ...
% 7.05/3.24 % External prover 'e' found a proof!
% 7.05/3.24 % [INFO] Killing All external provers ...
% 7.05/3.24 % Time passed: 2765ms (effective reasoning time: 2216ms)
% 7.05/3.24 % 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)>
% 7.05/3.24 % Axioms used in derivation (10): thm_2Epred__set_2EREST__DEF, logicdef_2E_3D, logicdef_2E_5C_2F, quantdef_2E_21, logicdef_2E_3D_3D_3E, thm_2Epred__set_2EIN__DELETE, logicdef_2E_7E, quantdef_2E_3F, thm_2Epred__set_2ESUBSET__DEF, logicdef_2E_2F_5C
% 7.05/3.24 % No. of inferences in proof: 43
% 7.05/3.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2765 ms resp. 2216 ms w/o parsing
% 7.28/3.36 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.28/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------