%------------------------------------------------------------------------------
% 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 : n006.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 07:35:45 AM UTC 2026
% Result : Theorem 74.81s 30.21s
% Output : Refutation 74.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 47 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 290 ( 23 ~; 8 |; 4 &; 246 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 15 ( 0 ^; 14 !; 0 ?; 15 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(del_type,type,
del: $tType ).
thf(tp__o_type,type,
tp__o: $tType ).
thf(tp__ty_2Enum_2Enum_type,type,
tp__ty_2Enum_2Enum: $tType ).
thf(tp__ty_2Erealax_2Ereal_type,type,
tp__ty_2Erealax_2Ereal: $tType ).
thf(tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal_type,type,
tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(inj__ty_2Enum_2Enum_decl,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
thf(c_2Enum_2E0_decl,type,
c_2Enum_2E0: $i ).
thf(fo__c_2Enum_2E0_decl,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
thf(inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal_decl,type,
inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal > $i ).
thf(surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal_decl,type,
surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $i > tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
thf(c_2Ecomplex_2Ecomplex__of__num_decl,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
thf(c_2Ecomplex_2Ecomplex__inv_decl,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
thf(sk1_decl,type,
sk1: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
thf(sk1_def,definition,
( sk1
= ( @+[A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
~ ( ( A
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ) ) ) ).
thf(1,conjecture,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( A
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(2,negated_conjecture,
~ ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( A
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( A
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,plain,
( ( ( sk1 @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
& ( sk1
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(50,plain,
( ( sk1 @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(52,plain,
( ( sk1 @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(41,axiom,
( ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum )
= c_2Enum_2E0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stp_eq_fo_c_2Enum_2E0) ).
thf(163,plain,
( ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum )
= c_2Enum_2E0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(164,plain,
( ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum )
= c_2Enum_2E0 ),
inference(lifteq,[status(thm)],[163]) ).
thf(211,plain,
( ( sk1 @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ),
inference(rewrite,[status(thm)],[52,164]) ).
thf(43,axiom,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
<=> ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0) ).
thf(168,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) )
& ( ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(169,plain,
( ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) )
& ! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
=> ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ) ),
inference(miniscope,[status(thm)],[168]) ).
thf(170,plain,
! [B: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( ( B @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( B
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) )
& ( ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(cnfConj,[status(thm)],[170]) ).
thf(173,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( A
= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(39591,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(rewrite,[status(thm)],[173,164]) ).
thf(39612,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( sk1 @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(paramod_ordered,[status(thm)],[211,39591]) ).
thf(39613,plain,
! [A: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( ( sk1 @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= ( A @ inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( c_2Ecomplex_2Ecomplex__inv @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) )
| ( A
= ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ) ),
inference(simp,[status(thm)],[39612]) ).
thf(39614,plain,
( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
= sk1 ),
inference(pattern_uni,[status(thm)],[39613:[bind(A,$thf( sk1 ))]]) ).
thf(49,plain,
( sk1
!= ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(51,plain,
( ( fo__c_2Enum_2E0 @ inj__ty_2Enum_2Enum @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= sk1 ),
inference(lifteq,[status(thm)],[49]) ).
thf(212,plain,
( ( c_2Enum_2E0 @ ( c_2Ecomplex_2Ecomplex__of__num @ ap ) @ surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal )
!= sk1 ),
inference(rewrite,[status(thm)],[51,164]) ).
thf(39774,plain,
$false,
inference(simplifyReflect,[status(thm)],[39614,212]) ).
%------------------------------------------------------------------------------
%----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
% 0.13/5.61 % Computer : n006.cluster.edu
% 0.13/5.61 % Model : x86_64 x86_64
% 0.13/5.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.61 % Memory : 8046.5625MB
% 0.13/5.61 % OS : Linux 6.8.0-71-generic
% 0.13/5.61 % CPULimit : 300
% 0.13/5.61 % WCLimit : 300
% 0.13/5.61 % DateTime : Fri Sep 25 17:28:19 UTC 2026
% 0.13/5.62 % CPUTime :
% 0.13/5.62 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
% 0.91/6.18 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/6.43 % [INFO] Parsing done (243ms).
% 1.64/6.44 % [INFO] Running in sequential loop mode.
% 2.41/6.85 % [INFO] eprover registered as external prover.
% 2.41/6.86 % [INFO] Scanning for conjecture ...
% 2.67/6.99 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 2.99/7.09 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 3.26/7.16 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.26/7.17 % [INFO] Type checking passed.
% 3.26/7.18 % [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 ...
% 74.81/30.21 % [INFO] Killing All external provers ...
% 74.81/30.21 % Time passed: 24446ms (effective reasoning time: 23755ms)
% 74.81/30.21 % 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)>
% 74.81/30.21 % Axioms used in derivation (2): stp_eq_fo_c_2Enum_2E0, conj_thm_2Ecomplex_2ECOMPLEX__INV__EQ__0
% 74.81/30.21 % No. of inferences in proof: 24
% 74.81/30.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24446 ms resp. 23755 ms w/o parsing
% 74.81/30.26 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 74.81/30.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------