%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP019+1 : 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 : n002.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 52.29s 15.85s
% Output : Refutation 52.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 40 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 556 ( 21 ~; 7 |; 4 &; 515 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 0 ^; 13 !; 0 ?; 14 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(s_decl,type,
s: $i > $i > $i ).
thf(tyop_2Epair_2Eprod_decl,type,
tyop_2Epair_2Eprod: $i > $i > $i ).
thf(tyop_2Erealax_2Ereal_decl,type,
tyop_2Erealax_2Ereal: $i ).
thf(c_2Ecomplex_2Ecomplex__of__num_2E1_decl,type,
c_2Ecomplex_2Ecomplex__of__num_2E1: $i > $i ).
thf(tyop_2Enum_2Enum_decl,type,
tyop_2Enum_2Enum: $i ).
thf(c_2Enum_2E0_2E0_decl,type,
c_2Enum_2E0_2E0: $i ).
thf(c_2Ecomplex_2Ecomplex__inv_2E1_decl,type,
c_2Ecomplex_2Ecomplex__inv_2E1: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(32,plain,
( ( ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
& ( ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(34,plain,
( ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
( ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
<=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(131,plain,
! [A: $i] :
( ( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) )
& ( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(132,plain,
( ! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) )
& ! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
=> ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ) ),
inference(miniscope,[status(thm)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( ( ( B @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
| ( ( B @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) )
& ( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
| ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(134,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
| ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
inference(cnfConj,[status(thm)],[133]) ).
thf(136,plain,
! [A: $i] :
( ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
| ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
inference(lifteq,[status(thm)],[134]) ).
thf(16649,plain,
! [A: $i] :
( ( ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
| ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
| ( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,136]) ).
thf(16650,plain,
! [A: $i] :
( ( ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) @ c_2Ecomplex_2Ecomplex__inv_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) )
| ( ( A @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ) ),
inference(simp,[status(thm)],[16649]) ).
thf(16651,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
= ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ),
inference(pattern_uni,[status(thm)],[16650:[bind(A,$thf( sk1 ))]]) ).
thf(33,plain,
( ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(35,plain,
( ( c_2Enum_2E0_2E0 @ ( tyop_2Enum_2Enum @ s ) @ c_2Ecomplex_2Ecomplex__of__num_2E1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) )
!= ( sk1 @ ( tyop_2Erealax_2Ereal @ ( tyop_2Erealax_2Ereal @ tyop_2Epair_2Eprod ) @ s ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(21353,plain,
$false,
inference(simplifyReflect,[status(thm)],[16651,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP019+1 : 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
% 0.13/0.40 % Computer : n002.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 17:31:07 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.83/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/1.19 % [INFO] Parsing done (212ms).
% 1.42/1.21 % [INFO] Running in sequential loop mode.
% 2.13/1.60 % [INFO] eprover registered as external prover.
% 2.13/1.61 % [INFO] Scanning for conjecture ...
% 2.30/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.49/1.81 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.73/1.90 % [INFO] Problem is first-order (TPTP FOF).
% 2.73/1.91 % [INFO] Type checking passed.
% 2.73/1.91 % [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 ...
% 52.29/15.84 % [INFO] Killing All external provers ...
% 52.29/15.85 % Time passed: 15293ms (effective reasoning time: 14628ms)
% 52.29/15.85 % 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)>
% 52.29/15.85 % Axioms used in derivation (1): thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 52.29/15.85 % No. of inferences in proof: 18
% 52.29/15.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15293 ms resp. 14628 ms w/o parsing
% 52.56/15.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.56/15.90 % [INFO] Killing All external provers ...
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