%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP019^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:05:15 AM UTC 2026
% Result : Theorem 11.87s 10.80s
% Output : CNFRefutation 11.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 25 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 308 ( 21 ~; 10 |; 1 &; 270 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 5 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 32 ( 0 ^; 32 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
del: $tType ).
thf(decl_sort2,type,
tp__ty_2Enum_2Enum: $tType ).
thf(decl_sort3,type,
tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal: $tType ).
thf(decl_25,type,
arr: del > del > del ).
thf(decl_26,type,
mem: $i > del > $o ).
thf(decl_27,type,
ap: $i > $i > $i ).
thf(decl_87,type,
ty_2Enum_2Enum: del ).
thf(decl_88,type,
inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i ).
thf(decl_91,type,
fo__c_2Enum_2E0: tp__ty_2Enum_2Enum ).
thf(decl_196,type,
ty_2Epair_2Eprod: del > del > del ).
thf(decl_2085,type,
ty_2Erealax_2Ereal: del ).
thf(decl_2327,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(decl_2328,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(decl_2589,type,
c_2Ecomplex_2Ecomplex__inv: $i ).
thf(decl_2592,type,
c_2Ecomplex_2Ecomplex__of__num: $i ).
thf(decl_2602,type,
esk1_0: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal ).
thf(ap_tp,axiom,
! [X3: del,X4: del,X5: $i] :
( ( mem @ X5 @ ( arr @ X3 @ X4 ) )
=> ! [X6: $i] :
( ( mem @ X6 @ X3 )
=> ( mem @ ( ap @ X5 @ X6 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',ap_tp) ).
thf(conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
! [X26849: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( X26849
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X26849 ) ) )
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ) ).
thf(stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,axiom,
! [X24059: $i] :
( ( mem @ X24059 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
=> ( X24059
= ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X24059 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).
thf(mem_c_2Ecomplex_2Ecomplex__of__num,axiom,
mem @ c_2Ecomplex_2Ecomplex__of__num @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',mem_c_2Ecomplex_2Ecomplex__of__num) ).
thf(mem_c_2Ecomplex_2Ecomplex__inv,axiom,
mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',mem_c_2Ecomplex_2Ecomplex__inv) ).
thf(stp_inj_mem_ty_2Enum_2Enum,axiom,
! [X147: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X147 ) @ ty_2Enum_2Enum ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',stp_inj_mem_ty_2Enum_2Enum) ).
thf(stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal,axiom,
! [X24058: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X24058 ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal) ).
thf(conj_thm_2Ecomplex_2ECOMPLEX__INV__0,axiom,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__0) ).
thf(conj_thm_2Ecomplex_2ECOMPLEX__INV__INV,axiom,
! [X26846: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X26846 ) ) ) )
= X26846 ),
file('/export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p',conj_thm_2Ecomplex_2ECOMPLEX__INV__INV) ).
thf(c_0_9,plain,
! [X27051: del,X27052: del,X27053: $i,X27054: $i] :
( ~ ( mem @ X27053 @ ( arr @ X27051 @ X27052 ) )
| ~ ( mem @ X27054 @ X27051 )
| ( mem @ ( ap @ X27053 @ X27054 ) @ X27052 ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
thf(c_0_10,negated_conjecture,
~ ! [X26849: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( X26849
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X26849 ) ) )
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).
thf(c_0_11,plain,
! [X27010: $i] :
( ~ ( mem @ X27010 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
| ( X27010
= ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X27010 ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[stp_iso_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal])])]) ).
thf(c_0_12,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( ap @ X2 @ X5 ) @ X4 )
| ~ ( mem @ X2 @ ( arr @ X3 @ X4 ) )
| ~ ( mem @ X5 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_13,plain,
mem @ c_2Ecomplex_2Ecomplex__of__num @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
inference(split_conjunct,[status(thm)],[mem_c_2Ecomplex_2Ecomplex__of__num]) ).
thf(c_0_14,negated_conjecture,
~ ! [X26849: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( X26849
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
=> ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X26849 ) ) )
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_10]) ).
thf(c_0_15,plain,
mem @ c_2Ecomplex_2Ecomplex__inv @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
inference(split_conjunct,[status(thm)],[mem_c_2Ecomplex_2Ecomplex__inv]) ).
thf(c_0_16,plain,
! [X2: $i] :
( ( X2
= ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X2 ) ) )
| ~ ( mem @ X2 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_17,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ X2 ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
| ~ ( mem @ X2 @ ty_2Enum_2Enum ) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_18,negated_conjecture,
( ( esk1_0
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
& ( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ esk1_0 ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
thf(c_0_19,plain,
! [X27116: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X27116 ) @ ty_2Enum_2Enum ),
inference(variable_rename,[status(thm)],[stp_inj_mem_ty_2Enum_2Enum]) ).
thf(c_0_20,plain,
! [X2: $i] :
( ( mem @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ X2 ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) )
| ~ ( mem @ X2 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
thf(c_0_21,plain,
! [X27009: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X27009 ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
inference(variable_rename,[status(thm)],[stp_inj_mem_c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal]) ).
thf(c_0_22,plain,
! [X2: $i] :
( ( ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ X2 ) ) )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ X2 ) )
| ~ ( mem @ X2 @ ty_2Enum_2Enum ) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
thf(c_0_23,negated_conjecture,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ esk1_0 ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_24,plain,
! [X146: tp__ty_2Enum_2Enum] : ( mem @ ( inj__ty_2Enum_2Enum @ X146 ) @ ty_2Enum_2Enum ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_25,plain,
! [X2: $i] :
( ( ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ X2 ) ) )
= ( ap @ c_2Ecomplex_2Ecomplex__inv @ X2 ) )
| ~ ( mem @ X2 @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ) ),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
thf(c_0_26,plain,
! [X24057: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] : ( mem @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X24057 ) @ ( ty_2Epair_2Eprod @ ty_2Erealax_2Ereal @ ty_2Erealax_2Ereal ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_27,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
inference(split_conjunct,[status(thm)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__0]) ).
thf(c_0_28,negated_conjecture,
( ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ esk1_0 ) ) ) )
= ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
thf(c_0_29,plain,
! [X24057: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X24057 ) ) ) )
= ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X24057 ) ) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
thf(c_0_30,plain,
! [X27021: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X27021 ) ) ) )
= X27021 ),
inference(variable_rename,[status(thm)],[conj_thm_2Ecomplex_2ECOMPLEX__INV__INV]) ).
thf(c_0_31,negated_conjecture,
( esk1_0
!= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
thf(c_0_32,plain,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )
= ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ esk1_0 ) ) ) ),
inference(rw,[status(thm)],[c_0_27,c_0_23]) ).
thf(c_0_33,negated_conjecture,
( ( ap @ c_2Ecomplex_2Ecomplex__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) )
= ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ esk1_0 ) ) ),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_34,plain,
! [X24057: tp__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal] :
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ X24057 ) ) ) )
= X24057 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_35,negated_conjecture,
( ( surj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ ( ap @ c_2Ecomplex_2Ecomplex__inv @ ( inj__c_ty_2Epair_2Eprod_ty_2Erealax_2Ereal_ty_2Erealax_2Ereal @ esk1_0 ) ) )
!= esk1_0 ),
inference(rw,[status(thm)],[c_0_31,c_0_23]) ).
thf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP019^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:33:16 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 6.10/6.15 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.YYSL2g7OuW/E---3.1_3108906.p
% 11.87/10.80 % Version: 3.5.1-ho
% 11.87/10.80 % Preprocessing class: HMLLSMLLSSLNSFA.
% 11.87/10.80 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 11.87/10.80 % Starting new_bool_8 with 1184s (4) cores
% 11.87/10.80 % Starting post_as_ho5 with 592s (2) cores
% 11.87/10.80 % Starting new_bool_9 with 296s (1) cores
% 11.87/10.80 % Starting new_bool_3 with 296s (1) cores
% 11.87/10.80 % post_as_ho5 with pid 3108920 completed with status 0
% 11.87/10.80 % Result found by post_as_ho5
% 11.87/10.80 % Preprocessing class: HMLLSMLLSSLNSFA.
% 11.87/10.80 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 11.87/10.80 % Starting new_bool_8 with 1184s (4) cores
% 11.87/10.80 % Starting post_as_ho5 with 592s (2) cores
% 11.87/10.80 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 11.87/10.80 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 11.87/10.80 % Search class: HGUSM-FSLM32-DSFFFFNN
% 11.87/10.80 % partial match(2): FGUSM-FSLM32-DFFFFFNN
% 11.87/10.80 % Scheduled 7 strats onto 2 cores with 592 seconds (592 total)
% 11.87/10.80 % Starting SubtermCWHack with 54s (1) cores
% 11.87/10.80 % Starting post_as_ho5 with 60s (1) cores
% 11.87/10.80 % SubtermCWHack with pid 3108923 completed with status 0
% 11.87/10.80 % Result found by SubtermCWHack
% 11.87/10.80 % Preprocessing class: HMLLSMLLSSLNSFA.
% 11.87/10.80 % Scheduled 4 strats onto 8 cores with 296 seconds (2368 total)
% 11.87/10.80 % Starting new_bool_8 with 1184s (4) cores
% 11.87/10.80 % Starting post_as_ho5 with 592s (2) cores
% 11.87/10.80 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true))
% 11.87/10.80 % SinE strategy is GSinE(CountFormulas,,true,1.0,0,2,20000,1.0,true)
% 11.87/10.80 % Search class: HGUSM-FSLM32-DSFFFFNN
% 11.87/10.80 % partial match(2): FGUSM-FSLM32-DFFFFFNN
% 11.87/10.80 % Scheduled 7 strats onto 2 cores with 592 seconds (592 total)
% 11.87/10.80 % Starting SubtermCWHack with 54s (1) cores
% 11.87/10.80 % Preprocessing time : 0.011 s
% 11.87/10.80
% 11.87/10.80 % Proof found!
% 11.87/10.80 % SZS status Theorem
% 11.87/10.80 % SZS output start CNFRefutation
% See solution above
% 11.87/10.80 % Parsed axioms : 17048
% 11.87/10.80 % Removed by relevancy pruning/SinE : 16976
% 11.87/10.80 % Initial clauses : 172
% 11.87/10.80 % Removed in clause preprocessing : 21
% 11.87/10.80 % Initial clauses in saturation : 151
% 11.87/10.80 % Processed clauses : 54
% 11.87/10.80 % ...of these trivial : 5
% 11.87/10.80 % ...subsumed : 1
% 11.87/10.80 % ...remaining for further processing : 48
% 11.87/10.80 % Other redundant clauses eliminated : 7
% 11.87/10.80 % Clauses deleted for lack of memory : 0
% 11.87/10.80 % Backward-subsumed : 0
% 11.87/10.80 % Backward-rewritten : 8
% 11.87/10.80 % Generated clauses : 100
% 11.87/10.80 % ...of the previous two non-redundant : 76
% 11.87/10.80 % ...aggressively subsumed : 0
% 11.87/10.80 % Contextual simplify-reflections : 0
% 11.87/10.80 % Paramodulations : 92
% 11.87/10.80 % Factorizations : 0
% 11.87/10.80 % NegExts : 0
% 11.87/10.80 % Equation resolutions : 8
% 11.87/10.80 % Disequality decompositions : 0
% 11.87/10.80 % Total rewrite steps : 73
% 11.87/10.80 % ...of those cached : 52
% 11.87/10.80 % Propositional unsat checks : 0
% 11.87/10.80 % Propositional check models : 0
% 11.87/10.80 % Propositional check unsatisfiable : 0
% 11.87/10.80 % Propositional clauses : 0
% 11.87/10.80 % Propositional clauses after purity: 0
% 11.87/10.80 % Propositional unsat core size : 0
% 11.87/10.80 % Propositional preprocessing time : 0.000
% 11.87/10.80 % Propositional encoding time : 0.000
% 11.87/10.80 % Propositional solver time : 0.000
% 11.87/10.80 % Success case prop preproc time : 0.000
% 11.87/10.80 % Success case prop encoding time : 0.000
% 11.87/10.80 % Success case prop solver time : 0.000
% 11.87/10.80 % Current number of processed clauses : 37
% 11.87/10.80 % Positive orientable unit clauses : 21
% 11.87/10.80 % Positive unorientable unit clauses: 0
% 11.87/10.80 % Negative unit clauses : 1
% 11.87/10.80 % Non-unit-clauses : 15
% 11.87/10.80 % Current number of unprocessed clauses: 170
% 11.87/10.80 % ...number of literals in the above : 625
% 11.87/10.80 % Current number of archived formulas : 0
% 11.87/10.80 % Current number of archived clauses : 8
% 11.87/10.80 % Clause-clause subsumption calls (NU) : 53
% 11.87/10.80 % Rec. Clause-clause subsumption calls : 53
% 11.87/10.80 % Non-unit clause-clause subsumptions : 1
% 11.87/10.80 % Unit Clause-clause subsumption calls : 0
% 11.87/10.80 % Rewrite failures with RHS unbound : 0
% 11.87/10.80 % BW rewrite match attempts : 15
% 11.87/10.80 % BW rewrite match successes : 5
% 11.87/10.80 % Condensation attempts : 0
% 11.87/10.80 % Condensation successes : 0
% 11.87/10.80 % Termbank termtop insertions : 1092740
% 11.87/10.80 % Search garbage collected termcells : 358910
% 11.87/10.80
% 11.87/10.80 % -------------------------------------------------
% 11.87/10.80 % User time : 0.181 s
% 11.87/10.80 % System time : 0.129 s
% 11.87/10.80 % Total time : 0.310 s
% 11.87/10.80 % Maximum resident set size: 75340 pages
% 11.87/10.80
% 11.87/10.80 % -------------------------------------------------
% 11.87/10.80 % User time : 4.417 s
% 11.87/10.80 % System time : 0.293 s
% 11.87/10.80 % Total time : 4.710 s
% 11.87/10.80 % Maximum resident set size: 69888 pages
% 11.87/10.80 % E exiting
%------------------------------------------------------------------------------