%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP019+2 : 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 : n010.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 : Sun Sep 27 07:35:44 AM UTC 2026
% Result : Theorem 74.10s 39.10s
% Output : Refutation 74.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 54 ( 37 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 227 ( 29 ~; 15 |; 4 &; 166 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 11 ( 0 ^; 10 !; 0 ?; 11 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(mem_decl,type,
mem: $i > $i > $o ).
thf(ty_2Epair_2Eprod_decl,type,
ty_2Epair_2Eprod: $i > $i > $i ).
thf(ty_2Erealax_2Ereal_decl,type,
ty_2Erealax_2Ereal: $i ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(c_2Ecomplex_2Ecomplex__of__num_decl,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
thf(c_2Enum_2E0_decl,type,
c_2Enum_2E0: $i ).
thf(c_2Ecomplex_2Ecomplex__inv_decl,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
=> ( ( A
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
=> ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
=> ( ( A
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
=> ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
=> ( ( A
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
=> ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i] :
( ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
=> ( ( A
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
=> ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,plain,
( ( ( sk1 @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
& ( sk1
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
& ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( sk1 @ mem ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(39,plain,
( ( sk1 @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ),
inference(cnfConj,[status(thm)],[36]) ).
thf(41,plain,
( ( sk1 @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(34,axiom,
! [A: $i] :
( ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
=> ( ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
<=> ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(123,plain,
! [A: $i] :
( ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
=> ( ( ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
=> ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) )
& ( ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
=> ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(124,plain,
! [A: $i] :
( ( ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ( A
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ~ ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) ) )
& ( ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ~ ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) ) ) ),
inference(cnf,[status(esa)],[123]) ).
thf(125,plain,
! [A: $i] :
( ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ~ ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) ) ),
inference(cnfConj,[status(thm)],[124]) ).
thf(127,plain,
! [A: $i] :
( ~ ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
| ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ( ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ),
inference(lifteq,[status(thm)],[125]) ).
thf(36857,plain,
! [A: $i] :
( ( ( sk1 @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) ) )
| ~ ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
| ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) )
| ( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,127]) ).
thf(36858,plain,
! [A: $i] :
( ( ( sk1 @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) )
!= ( A @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) ) )
| ~ ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( A @ mem ) )
| ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ) ),
inference(simp,[status(thm)],[36857]) ).
thf(36859,plain,
( ~ ( ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( sk1 @ mem ) )
| ( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) )
= sk1 ) ),
inference(pattern_uni,[status(thm)],[36858:[bind(A,$thf( sk1 ))]]) ).
thf(37,plain,
ty_2Erealax_2Ereal @ ( ty_2Erealax_2Ereal @ ty_2Epair_2Eprod ) @ ( sk1 @ mem ),
inference(cnfConj,[status(thm)],[36]) ).
thf(49535,plain,
( ~ $true
| ( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) )
= sk1 ) ),
inference(rewrite,[status(thm)],[36859,37]) ).
thf(49536,plain,
( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) )
= sk1 ),
inference(simp,[status(thm)],[49535]) ).
thf(38,plain,
( sk1
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) ) ),
inference(cnfConj,[status(thm)],[36]) ).
thf(40,plain,
( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) )
!= sk1 ),
inference(lifteq,[status(thm)],[38]) ).
thf(49537,plain,
$false,
inference(simplifyReflect,[status(thm)],[49536,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+2 : 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
% 0.14/5.42 % Computer : n010.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.42 % CPULimit : 300
% 0.14/5.42 % WCLimit : 300
% 0.14/5.42 % DateTime : Fri Sep 25 17:28:36 UTC 2026
% 0.14/5.42 % CPUTime :
% 0.14/5.42 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
% 0.19/6.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/6.23 % [INFO] Parsing done (216ms).
% 1.32/6.25 % [INFO] Running in sequential loop mode.
% 1.99/6.64 % [INFO] eprover registered as external prover.
% 1.99/6.65 % [INFO] Scanning for conjecture ...
% 2.18/6.76 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 2.35/6.84 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.35/6.90 % [INFO] Problem is first-order (TPTP FOF).
% 2.56/6.90 % [INFO] Type checking passed.
% 2.56/6.91 % [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 ...
% 74.10/39.09 % [INFO] Killing All external provers ...
% 74.10/39.10 % Time passed: 33524ms (effective reasoning time: 32841ms)
% 74.10/39.10 % 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)>
% 74.10/39.10 % Axioms used in derivation (1): conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 74.10/39.10 % No. of inferences in proof: 20
% 74.10/39.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 33524 ms resp. 32841 ms w/o parsing
% 74.10/39.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 74.10/39.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------