%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP013^3 : 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 : n005.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 08:06:21 AM UTC 2026
% Result : Theorem 6.64s 2.64s
% Output : Refutation 6.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 21 unt; 0 typ; 2 def)
% Number of atoms : 140 ( 68 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 357 ( 19 ~; 0 |; 32 &; 282 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 86 ( 0 ^; 84 !; 0 ?; 86 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(skt1_type,type,
skt1: $tType ).
thf(c_2Earithmetic_2E_2B_decl,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_2D_decl,type,
c_2Earithmetic_2E_2D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Earithmetic_2E_3C_3D_decl,type,
c_2Earithmetic_2E_3C_3D: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2ECOND_decl,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $o ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $o ).
thf(c_2Ewords_2En2w_decl,type,
c_2Ewords_2En2w:
!>[TA: $tType] : ( tyop_2Enum_2Enum > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__2comp_decl,type,
c_2Ewords_2Eword__2comp:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__add_decl,type,
c_2Ewords_2Eword__add:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(c_2Ewords_2Eword__sub_decl,type,
c_2Ewords_2Eword__sub:
!>[TA: $tType] : ( ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) > ( tyop_2Efcp_2Ecart @ $o @ TA ) ) ).
thf(sk1_decl,type,
sk1: tyop_2Enum_2Enum ).
thf(sk2_decl,type,
sk2: tyop_2Enum_2Enum ).
thf(sk1_def,definition,
( sk1
= ( @+[A: tyop_2Enum_2Enum] :
~ ! [B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ skt1 @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ A ) @ ( c_2Ewords_2En2w @ skt1 @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: tyop_2Enum_2Enum] :
~ ( ( c_2Earithmetic_2E_3C_3D @ A @ sk1 )
=> ( ( c_2Ewords_2En2w @ skt1 @ ( c_2Earithmetic_2E_2D @ sk1 @ A ) )
= ( c_2Ewords_2Eword__sub @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ sk1 ) @ ( c_2Ewords_2En2w @ skt1 @ A ) ) ) ) ) ) ).
thf(5,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ( ~ A ) )
& ( ( A = c_2Ebool_2EF )
= ( ~ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
thf(29,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET = A )
= A )
& ( ( A = c_2Ebool_2ET )
= A )
& ( ( c_2Ebool_2EF = A )
= ( ~ A ) )
& ( ( A = c_2Ebool_2EF )
= ( ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [TA: $tType,A: TA] :
( ( A = A )
= c_2Ebool_2ET ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE) ).
thf(28,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TB @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
= ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2B @ A @ B ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Earithmetic_2E_3C_3D @ B @ A ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD) ).
thf(65,plain,
! [TA: $tType,TB: $tType] :
( ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TB @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ A ) ) @ ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ B ) ) )
= ( c_2Ewords_2Eword__2comp @ TB @ ( c_2Ewords_2En2w @ TB @ ( c_2Earithmetic_2E_2B @ A @ B ) ) ) )
& ! [A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Ewords_2Eword__add @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ B ) ) )
= ( c_2Ebool_2ECOND @ ( tyop_2Efcp_2Ecart @ $o @ TA ) @ ( c_2Earithmetic_2E_3C_3D @ B @ A ) @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) ) @ ( c_2Ewords_2Eword__2comp @ TA @ ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& ( ( A
=> A )
= c_2Ebool_2ET )
& ( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(16,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
( ( ( c_2Ebool_2ET
=> $true )
= $true )
& ( ( $true
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> $true )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( $true
=> c_2Ebool_2EF )
= ( ~ $true ) ) ),
inference(instance,[status(thm)],[16]) ).
thf(18,plain,
( c_2Ebool_2ET
& c_2Ebool_2ET
& ~ c_2Ebool_2EF ),
inference(simp,[status(thm)],[17]) ).
thf(21,plain,
( c_2Ebool_2ET
& c_2Ebool_2ET
& ~ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[18]) ).
thf(22,plain,
c_2Ebool_2ET,
inference(cnfConj,[status(thm)],[21]) ).
thf(7,axiom,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm) ).
thf(41,plain,
! [TA: $tType] :
( ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ! [A: TA,B: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(42,plain,
! [TA: $tType,D: TA,C: TA,B: TA,A: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ C @ D )
= D ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(cnfConj,[status(thm)],[42]) ).
thf(45,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(lifteq,[status(thm)],[43]) ).
thf(81,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $true @ A @ B )
= A ),
inference(rewrite,[status(thm)],[45,22]) ).
thf(8,axiom,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CONG) ).
thf(48,plain,
! [TA: $tType,A: $o,B: $o,C: TA,D: TA,E: TA,F: TA] :
( ( ( A = B )
& ( B
=> ( C = D ) )
& ( ~ B
=> ( E = F ) ) )
=> ( ( c_2Ebool_2ECOND @ TA @ A @ C @ E )
= ( c_2Ebool_2ECOND @ TA @ B @ D @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub) ).
thf(2,negated_conjecture,
~ ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [TA: $tType,A: tyop_2Enum_2Enum,B: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ B @ A )
=> ( ( c_2Ewords_2En2w @ TA @ ( c_2Earithmetic_2E_2D @ A @ B ) )
= ( c_2Ewords_2Eword__sub @ TA @ ( c_2Ewords_2En2w @ TA @ A ) @ ( c_2Ewords_2En2w @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(cnfConj,[status(thm)],[42]) ).
thf(46,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(lifteq,[status(thm)],[44]) ).
thf(47,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(simp,[status(thm)],[46]) ).
thf(23,plain,
~ c_2Ebool_2EF,
inference(cnfConj,[status(thm)],[21]) ).
thf(82,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
= B ),
inference(rewrite,[status(thm)],[47,23]) ).
thf(12,plain,
( ( c_2Earithmetic_2E_3C_3D @ sk2 @ sk1 )
& ( ( c_2Ewords_2En2w @ skt1 @ ( c_2Earithmetic_2E_2D @ sk1 @ sk2 ) )
!= ( c_2Ewords_2Eword__sub @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ sk1 ) @ ( c_2Ewords_2En2w @ skt1 @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
c_2Earithmetic_2E_3C_3D @ sk2 @ sk1,
inference(cnfConj,[status(thm)],[12]) ).
thf(6,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(40,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,plain,
( ( c_2Ewords_2En2w @ skt1 @ ( c_2Earithmetic_2E_2D @ sk1 @ sk2 ) )
!= ( c_2Ewords_2Eword__sub @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ sk1 ) @ ( c_2Ewords_2En2w @ skt1 @ sk2 ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(15,plain,
( ( c_2Ewords_2En2w @ skt1 @ ( c_2Earithmetic_2E_2D @ sk1 @ sk2 ) )
!= ( c_2Ewords_2Eword__sub @ skt1 @ ( c_2Ewords_2En2w @ skt1 @ sk1 ) @ ( c_2Ewords_2En2w @ skt1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(9,axiom,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def) ).
thf(62,plain,
! [TA: $tType,A: tyop_2Efcp_2Ecart @ $o @ TA,B: tyop_2Efcp_2Ecart @ $o @ TA] :
( ( c_2Ewords_2Eword__sub @ TA @ A @ B )
= ( c_2Ewords_2Eword__add @ TA @ A @ ( c_2Ewords_2Eword__2comp @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(141,plain,
$false,
inference(e,[status(thm)],[29,28,65,22,81,48,16,11,82,13,41,40,23,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.10/0.21 % Computer : n005.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % 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 19:27:01 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
% 0.74/0.60 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/0.81 % [INFO] Parsing done (201ms).
% 1.45/0.82 % [INFO] Running in sequential loop mode.
% 2.43/1.20 % [INFO] eprover registered as external prover.
% 2.43/1.21 % [INFO] Scanning for conjecture ...
% 2.61/1.37 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.82/1.47 % [INFO] Axiom selection finished. Selected 8 axioms (removed 10 axioms).
% 3.11/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 3.11/1.54 % [INFO] Type checking passed.
% 3.11/1.54 % [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 ...
% 6.64/2.63 % External prover 'e' found a proof!
% 6.64/2.63 % [INFO] Killing All external provers ...
% 6.64/2.63 % Time passed: 2328ms (effective reasoning time: 1807ms)
% 6.64/2.63 % 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)>
% 6.64/2.63 % Axioms used in derivation (8): thm_2Ebool_2EEQ__CLAUSES, thm_2Ewords_2EWORD__LITERAL__ADD, thm_2Ebool_2ECOND__CONG, thm_2Ebool_2Ebool__case__thm, thm_2Ewords_2Eword__sub__def, thm_2Ebool_2EREFL__CLAUSE, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH
% 6.64/2.63 % No. of inferences in proof: 37
% 6.64/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2328 ms resp. 1807 ms w/o parsing
% 6.91/2.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.91/2.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------