%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP019^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:04:05 AM UTC 2026
% Result : Theorem 5.08s 4.81s
% Output : CNFRefutation 5.08s
% 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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.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
% 0.00/0.01 % Problem : ITP019^5 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 19:33:05 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 2.54/2.69 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.rOizDD8a3m/E---3.1_575994.p
% 5.08/4.81 % Version: 3.5.1-ho
% 5.08/4.81 % Preprocessing class: HMLLSMLLSSLNSFA.
% 5.08/4.81 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 5.08/4.81 % Starting new_bool_8 with 1196s (4) cores
% 5.08/4.81 % Starting post_as_ho5 with 598s (2) cores
% 5.08/4.81 % Starting new_bool_9 with 299s (1) cores
% 5.08/4.81 % Starting new_bool_3 with 299s (1) cores
% 5.08/4.81 % new_bool_9 with pid 576009 completed with status 0
% 5.08/4.81 % Result found by new_bool_9
% 5.08/4.81 % Preprocessing class: HMLLSMLLSSLNSFA.
% 5.08/4.81 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 5.08/4.81 % Starting new_bool_8 with 1196s (4) cores
% 5.08/4.81 % Starting post_as_ho5 with 598s (2) cores
% 5.08/4.81 % Starting new_bool_9 with 299s (1) cores
% 5.08/4.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 5.08/4.81 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 5.08/4.81 % Search class: HGUSM-FSLM32-DSFFFFNN
% 5.08/4.81 % partial match(2): FGUSM-FSLM32-DFFFFFNN
% 5.08/4.81 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 5.08/4.81 % Starting SubtermCWHack with 27s (1) cores
% 5.08/4.81 % SubtermCWHack with pid 576017 completed with status 0
% 5.08/4.81 % Result found by SubtermCWHack
% 5.08/4.81 % Preprocessing class: HMLLSMLLSSLNSFA.
% 5.08/4.81 % Scheduled 4 strats onto 8 cores with 299 seconds (2392 total)
% 5.08/4.81 % Starting new_bool_8 with 1196s (4) cores
% 5.08/4.81 % Starting post_as_ho5 with 598s (2) cores
% 5.08/4.81 % Starting new_bool_9 with 299s (1) cores
% 5.08/4.81 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1,,2,20000,1.0))
% 5.08/4.81 % SinE strategy is GSinE(CountFormulas,hypos,1,,2,20000,1.0)
% 5.08/4.81 % Search class: HGUSM-FSLM32-DSFFFFNN
% 5.08/4.81 % partial match(2): FGUSM-FSLM32-DFFFFFNN
% 5.08/4.81 % Scheduled 7 strats onto 1 cores with 299 seconds (299 total)
% 5.08/4.81 % Starting SubtermCWHack with 27s (1) cores
% 5.08/4.81 % Preprocessing time : 0.007 s
% 5.08/4.81
% 5.08/4.81 % Proof found!
% 5.08/4.81 % SZS status Theorem
% 5.08/4.81 % SZS output start CNFRefutation
% See solution above
% 5.08/4.81 % Parsed axioms : 17048
% 5.08/4.81 % Removed by relevancy pruning/SinE : 16976
% 5.08/4.81 % Initial clauses : 172
% 5.08/4.81 % Removed in clause preprocessing : 21
% 5.08/4.81 % Initial clauses in saturation : 151
% 5.08/4.81 % Processed clauses : 54
% 5.08/4.81 % ...of these trivial : 5
% 5.08/4.81 % ...subsumed : 1
% 5.08/4.81 % ...remaining for further processing : 48
% 5.08/4.81 % Other redundant clauses eliminated : 7
% 5.08/4.81 % Clauses deleted for lack of memory : 0
% 5.08/4.81 % Backward-subsumed : 0
% 5.08/4.81 % Backward-rewritten : 8
% 5.08/4.81 % Generated clauses : 100
% 5.08/4.81 % ...of the previous two non-redundant : 76
% 5.08/4.81 % ...aggressively subsumed : 0
% 5.08/4.81 % Contextual simplify-reflections : 0
% 5.08/4.81 % Paramodulations : 92
% 5.08/4.81 % Factorizations : 0
% 5.08/4.81 % NegExts : 0
% 5.08/4.81 % Equation resolutions : 8
% 5.08/4.81 % Disequality decompositions : 0
% 5.08/4.81 % Total rewrite steps : 73
% 5.08/4.81 % ...of those cached : 52
% 5.08/4.81 % Propositional unsat checks : 0
% 5.08/4.81 % Propositional check models : 0
% 5.08/4.81 % Propositional check unsatisfiable : 0
% 5.08/4.81 % Propositional clauses : 0
% 5.08/4.81 % Propositional clauses after purity: 0
% 5.08/4.81 % Propositional unsat core size : 0
% 5.08/4.81 % Propositional preprocessing time : 0.000
% 5.08/4.81 % Propositional encoding time : 0.000
% 5.08/4.81 % Propositional solver time : 0.000
% 5.08/4.81 % Success case prop preproc time : 0.000
% 5.08/4.81 % Success case prop encoding time : 0.000
% 5.08/4.81 % Success case prop solver time : 0.000
% 5.08/4.81 % Current number of processed clauses : 37
% 5.08/4.81 % Positive orientable unit clauses : 21
% 5.08/4.81 % Positive unorientable unit clauses: 0
% 5.08/4.81 % Negative unit clauses : 1
% 5.08/4.81 % Non-unit-clauses : 15
% 5.08/4.81 % Current number of unprocessed clauses: 170
% 5.08/4.81 % ...number of literals in the above : 625
% 5.08/4.81 % Current number of archived formulas : 0
% 5.08/4.81 % Current number of archived clauses : 8
% 5.08/4.81 % Clause-clause subsumption calls (NU) : 53
% 5.08/4.81 % Rec. Clause-clause subsumption calls : 53
% 5.08/4.81 % Non-unit clause-clause subsumptions : 1
% 5.08/4.81 % Unit Clause-clause subsumption calls : 0
% 5.08/4.81 % Rewrite failures with RHS unbound : 0
% 5.08/4.81 % BW rewrite match attempts : 15
% 5.08/4.81 % BW rewrite match successes : 5
% 5.08/4.81 % Condensation attempts : 0
% 5.08/4.81 % Condensation successes : 0
% 5.08/4.81 % Termbank termtop insertions : 1092740
% 5.08/4.81 % Search garbage collected termcells : 358910
% 5.08/4.81
% 5.08/4.81 % -------------------------------------------------
% 5.08/4.81 % User time : 0.164 s
% 5.08/4.81 % System time : 0.099 s
% 5.08/4.81 % Total time : 0.263 s
% 5.08/4.81 % Maximum resident set size: 75084 pages
% 5.08/4.81
% 5.08/4.81 % -------------------------------------------------
% 5.08/4.81 % User time : 1.927 s
% 5.08/4.81 % System time : 0.175 s
% 5.08/4.81 % Total time : 2.101 s
% 5.08/4.81 % Maximum resident set size: 69632 pages
% 5.08/4.81 % E exiting
%------------------------------------------------------------------------------