%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP019^3 : 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 : n018.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 08:06:24 AM UTC 2026
% Result : Theorem 4.66s 2.46s
% Output : Refutation 5.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 38 ( 27 unt; 0 typ; 1 def)
% Number of atoms : 113 ( 51 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 136 ( 25 ~; 2 |; 19 &; 71 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 43 ( 0 ^; 40 !; 2 ?; 43 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Enum_2Enum_type,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Erealax_2Ereal_type,type,
tyop_2Erealax_2Ereal: $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_2Enum_2E0_decl,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
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_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $o ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $o ).
thf(c_2Ebool_2E_5C_2F_decl,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ecomplex_2Ecomplex__inv_decl,type,
c_2Ecomplex_2Ecomplex__inv: ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) > ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ).
thf(c_2Ecomplex_2Ecomplex__of__num_decl,type,
c_2Ecomplex_2Ecomplex__of__num: tyop_2Enum_2Enum > ( tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ) ).
thf(c_2Ebool_2E_7E_decl,type,
c_2Ebool_2E_7E: $o > $o ).
thf(sk1_decl,type,
sk1: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal ).
thf(sk1_def,definition,
( sk1
= ( @+[A: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
~ ( ( A
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Ecomplex_2Ecomplex__inv @ A )
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ) ) ) ).
thf(5,axiom,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ( ~ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',logicdef_2E_7E) ).
thf(38,plain,
! [A: $o] :
( ( c_2Ebool_2E_7E @ A )
= ( ~ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,plain,
( ( c_2Ebool_2E_7E @ $false )
= ( ~ $false ) ),
inference(instance,[status(thm)],[38]) ).
thf(42,plain,
c_2Ebool_2E_7E @ $false,
inference(simp,[status(thm)],[41]) ).
thf(10,axiom,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(61,plain,
c_2Ebool_2ET,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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(43,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(11,axiom,
! [TA: $tType,A: $o] :
( ( ! [B: TA] : A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFORALL__SIMP) ).
thf(62,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(52,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(1,conjecture,
! [A: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
( ( A
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Ecomplex_2Ecomplex__inv @ A )
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
( ( A
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Ecomplex_2Ecomplex__inv @ A )
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
( ( A
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
=> ( ( c_2Ecomplex_2Ecomplex__inv @ A )
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
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(20,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_2F_5C @ A @ B )
= ( A
& B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
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(29,plain,
! [A: $o,B: $o] :
( ( c_2Ebool_2E_5C_2F @ A @ B )
= ( A
| B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,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(63,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)],[12]) ).
thf(64,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)],[63]) ).
thf(65,plain,
( c_2Ebool_2ET
& c_2Ebool_2ET
& ~ c_2Ebool_2EF ),
inference(simp,[status(thm)],[64]) ).
thf(68,plain,
( c_2Ebool_2ET
& c_2Ebool_2ET
& ~ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[65]) ).
thf(70,plain,
~ c_2Ebool_2EF,
inference(cnfConj,[status(thm)],[68]) ).
thf(15,plain,
( ( sk1
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
& ( ( c_2Ecomplex_2Ecomplex__inv @ sk1 )
= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( sk1
!= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(18,plain,
( ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 )
!= sk1 ),
inference(lifteq,[status(thm)],[16]) ).
thf(39,plain,
( ( c_2Ebool_2E_7E @ $true )
= ( ~ $true ) ),
inference(instance,[status(thm)],[38]) ).
thf(40,plain,
~ ( c_2Ebool_2E_7E @ $true ),
inference(simp,[status(thm)],[39]) ).
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(55,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(13,axiom,
! [A: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
( ( ( c_2Ecomplex_2Ecomplex__inv @ A )
= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(75,plain,
! [A: tyop_2Epair_2Eprod @ tyop_2Erealax_2Ereal @ tyop_2Erealax_2Ereal] :
( ( ( c_2Ecomplex_2Ecomplex__inv @ A )
= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) )
= ( A
= ( c_2Ecomplex_2Ecomplex__of__num @ c_2Enum_2E0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[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(58,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(100,plain,
$false,
inference(e,[status(thm)],[42,61,43,62,52,14,20,29,38,70,63,18,40,55,75,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:35:27 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (209ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 2.22/1.42 % [INFO] eprover registered as external prover.
% 2.22/1.43 % [INFO] Scanning for conjecture ...
% 2.41/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 2.41/1.56 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 2.41/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.60/1.60 % [INFO] Type checking passed.
% 2.60/1.60 % [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 ...
% 4.66/2.45 % External prover 'e' found a proof!
% 4.66/2.46 % [INFO] Killing All external provers ...
% 4.66/2.46 % Time passed: 2119ms (effective reasoning time: 1439ms)
% 4.66/2.46 % 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)>
% 4.66/2.46 % Axioms used in derivation (11): logicdef_2E_3D, logicdef_2E_5C_2F, logicdef_2E_3D_3D_3E, thm_2Ecomplex_2ECOMPLEX__INV__EQ__0, thm_2Ebool_2EFORALL__SIMP, logicdef_2E_2F_5C, logicdef_2E_7E, quantdef_2E_3F, quantdef_2E_21, thm_2Ebool_2EIMP__CLAUSES, thm_2Ebool_2ETRUTH
% 4.66/2.46 % No. of inferences in proof: 37
% 4.66/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2119 ms resp. 1439 ms w/o parsing
% 5.05/2.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.05/2.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------