TSTP Solution File: ITP387_1 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : ITP387_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat May  4 08:10:38 EDT 2024

% Result   : Theorem 31.12s 4.54s
% Output   : CNFRefutation 31.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   69
% Syntax   : Number of formulae    :   96 (  32 unt;  60 typ;   0 def)
%            Number of atoms       :   42 (  41 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   14 (   8   ~;   4   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :   25 (  25 usr)
%            Number of type conns  :   41 (  24   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   35 (  35 usr;  11 con; 0-2 aty)
%            Number of variables   :   78 (   0 sgn  77   !;   1   ?;  78   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_sort1,type,
    'A_ell2$': $tType ).

tff(decl_sort2,type,
    'C$': $tType ).

tff(decl_sort3,type,
    'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_fun_fun$': $tType ).

tff(decl_sort4,type,
    'A_c_prod_ell2_b_d_prod_ell2_cblinfun$': $tType ).

tff(decl_sort5,type,
    'A_c_prod_ell2_b_d_prod_ell2_fun$': $tType ).

tff(decl_sort6,type,
    'A_c_prod_ell2$': $tType ).

tff(decl_sort7,type,
    'C_ell2$': $tType ).

tff(decl_sort8,type,
    'C_ell2_d_ell2_cblinfun$': $tType ).

tff(decl_sort9,type,
    'A_c_prod$': $tType ).

tff(decl_sort10,type,
    'A$': $tType ).

tff(decl_sort11,type,
    'D_ell2$': $tType ).

tff(decl_sort12,type,
    'B_d_prod_ell2$': $tType ).

tff(decl_sort13,type,
    'A_ell2_b_ell2_cblinfun$': $tType ).

tff(decl_sort14,type,
    'A_ell2_b_ell2_fun$': $tType ).

tff(decl_sort15,type,
    'B_ell2$': $tType ).

tff(decl_sort16,type,
    'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun$': $tType ).

tff(decl_sort17,type,
    'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun_fun$': $tType ).

tff(decl_sort18,type,
    'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun$': $tType ).

tff(decl_sort19,type,
    'C_a_c_prod_fun$': $tType ).

tff(decl_sort20,type,
    'A_c_a_c_prod_fun_fun$': $tType ).

tff(decl_sort21,type,
    'C_ell2_d_ell2_fun$': $tType ).

tff(decl_sort22,type,
    'C_a_prod$': $tType ).

tff(decl_sort23,type,
    'A_c_prod_a_c_prod_ell2_fun$': $tType ).

tff(decl_sort24,type,
    'A_c_prod_c_a_prod_fun$': $tType ).

tff(decl_sort25,type,
    'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun_fun$': $tType ).

tff(decl_28,type,
    'fst$e': 'A_c_prod$' > 'A$' ).

tff(decl_43,type,
    'cblinfun_apply$': 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_fun_fun$' ).

tff(decl_59,type,
    'fun_app$q': ( 'A_c_a_c_prod_fun_fun$' * 'A$' ) > 'C_a_c_prod_fun$' ).

tff(decl_63,type,
    'b2$': 'C_ell2_d_ell2_cblinfun$' ).

tff(decl_71,type,
    'fun_app$l': ( 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_fun_fun$' * 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_fun$' ).

tff(decl_72,type,
    'tensor_ell2$': ( 'B_ell2$' * 'D_ell2$' ) > 'B_d_prod_ell2$' ).

tff(decl_84,type,
    'fun_app$t': ( 'A_ell2_b_ell2_fun$' * 'A_ell2$' ) > 'B_ell2$' ).

tff(decl_88,type,
    'fun_app$u': ( 'C_ell2_d_ell2_fun$' * 'C_ell2$' ) > 'D_ell2$' ).

tff(decl_98,type,
    'b1$': 'C_ell2_d_ell2_cblinfun$' ).

tff(decl_106,type,
    'plus$u': ( 'B_d_prod_ell2$' * 'B_d_prod_ell2$' ) > 'B_d_prod_ell2$' ).

tff(decl_107,type,
    'i$': 'A$' ).

tff(decl_114,type,
    'snd$e': 'A_c_prod$' > 'C$' ).

tff(decl_118,type,
    'ket$': 'A_c_prod_a_c_prod_ell2_fun$' ).

tff(decl_127,type,
    'cblinfun_apply$a': 'A_ell2_b_ell2_cblinfun$' > 'A_ell2_b_ell2_fun$' ).

tff(decl_134,type,
    'a$': 'A_ell2_b_ell2_cblinfun$' ).

tff(decl_140,type,
    'fun_app$s': ( 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun_fun$' * 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun$' ).

tff(decl_162,type,
    'fun_app$m': ( 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun$' * 'C_ell2_d_ell2_cblinfun$' ) > 'C_ell2_d_ell2_cblinfun$' ).

tff(decl_183,type,
    'plus$a': 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun_fun$' ).

tff(decl_200,type,
    'plus$b': 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun_fun$' ).

tff(decl_201,type,
    'fun_app$p': ( 'C_a_c_prod_fun$' * 'C$' ) > 'A_c_prod$' ).

tff(decl_215,type,
    'pair$': 'A_c_a_c_prod_fun_fun$' ).

tff(decl_217,type,
    'fun_app$n': ( 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun_fun$' * 'C_ell2_d_ell2_cblinfun$' ) > 'C_ell2_d_ell2_cblinfun_c_ell2_d_ell2_cblinfun_fun$' ).

tff(decl_223,type,
    'cblinfun_apply$b': 'C_ell2_d_ell2_cblinfun$' > 'C_ell2_d_ell2_fun$' ).

tff(decl_231,type,
    'tensor_op$': ( 'A_ell2_b_ell2_cblinfun$' * 'C_ell2_d_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ).

tff(decl_234,type,
    'swap$d': 'A_c_prod_c_a_prod_fun$' ).

tff(decl_268,type,
    'fun_app$ah': ( 'A_c_prod_c_a_prod_fun$' * 'A_c_prod$' ) > 'C_a_prod$' ).

tff(decl_269,type,
    'fun_app$o': ( 'A_c_prod_a_c_prod_ell2_fun$' * 'A_c_prod$' ) > 'A_c_prod_ell2$' ).

tff(decl_270,type,
    'ket$a': 'A$' > 'A_ell2$' ).

tff(decl_282,type,
    'plus$i': ( 'D_ell2$' * 'D_ell2$' ) > 'D_ell2$' ).

tff(decl_304,type,
    'fun_app$k': ( 'A_c_prod_ell2_b_d_prod_ell2_fun$' * 'A_c_prod_ell2$' ) > 'B_d_prod_ell2$' ).

tff(decl_314,type,
    'ket$b': 'C$' > 'C_ell2$' ).

tff(decl_342,type,
    'fun_app$r': ( 'A_c_prod_ell2_b_d_prod_ell2_cblinfun_a_c_prod_ell2_b_d_prod_ell2_cblinfun_fun$' * 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ) > 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$' ).

tff(decl_356,type,
    'j$': 'C$' ).

tff(decl_358,type,
    'fst$d': 'C_a_prod$' > 'C$' ).

tff(decl_477,type,
    esk111_2: ( 'C$' * 'A_c_prod$' ) > 'A$' ).

tff(axiom407,axiom,
    ! [X1160: 'C$',X1161: 'A_c_prod$'] :
      ( ( X1160 = 'snd$e'(X1161) )
    <=> ? [X1162: 'A$'] : ( X1161 = 'fun_app$p'('fun_app$q'('pair$',X1162),X1160) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom407) ).

tff(axiom430,axiom,
    ! [X1206: 'A_c_prod$'] : ( 'fst$d'('fun_app$ah'('swap$d',X1206)) = 'snd$e'(X1206) ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom430) ).

tff(conjecture9,conjecture,
    'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',conjecture9) ).

tff(axiom349,axiom,
    ! [X993: 'A$',X994: 'C$'] : ( 'fst$e'('fun_app$p'('fun_app$q'('pair$',X993),X994)) = X993 ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom349) ).

tff(axiom20,axiom,
    ! [X59: 'A_ell2_b_ell2_cblinfun$',X60: 'C_ell2_d_ell2_cblinfun$',X61: 'A$',X62: 'C$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'(X59,X60)),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X61),X62))) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X59),'ket$a'(X61)),'fun_app$u'('cblinfun_apply$b'(X60),'ket$b'(X62))) ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom20) ).

tff(axiom34,axiom,
    ! [X111: 'C_ell2_d_ell2_cblinfun$',X112: 'C_ell2_d_ell2_cblinfun$',X113: 'C_ell2$'] : ( 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a',X111),X112)),X113) = 'plus$i'('fun_app$u'('cblinfun_apply$b'(X111),X113),'fun_app$u'('cblinfun_apply$b'(X112),X113)) ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom34) ).

tff(axiom35,axiom,
    ! [X114: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X115: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X116: 'A_c_prod_ell2$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b',X114),X115)),X116) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$',X114),X116),'fun_app$k'('fun_app$l'('cblinfun_apply$',X115),X116)) ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom35) ).

tff(axiom337,axiom,
    ! [X964: 'A$',X965: 'C$'] : ( 'snd$e'('fun_app$p'('fun_app$q'('pair$',X964),X965)) = X965 ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom337) ).

tff(axiom95,axiom,
    ! [X293: 'B_ell2$',X294: 'D_ell2$',X295: 'D_ell2$'] : ( 'tensor_ell2$'(X293,'plus$i'(X294,X295)) = 'plus$u'('tensor_ell2$'(X293,X294),'tensor_ell2$'(X293,X295)) ),
    file('/export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p',axiom95) ).

tff(c_0_9,plain,
    ! [X2987: 'C$',X2988: 'A_c_prod$',X2990: 'C$',X2991: 'A_c_prod$',X2992: 'A$'] :
      ( ( ( X2987 != 'snd$e'(X2988) )
        | ( X2988 = 'fun_app$p'('fun_app$q'('pair$',esk111_2(X2987,X2988)),X2987) ) )
      & ( ( X2991 != 'fun_app$p'('fun_app$q'('pair$',X2992),X2990) )
        | ( X2990 = 'snd$e'(X2991) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom407])])])])])]) ).

tff(c_0_10,plain,
    ! [X3057: 'A_c_prod$'] : ( 'fst$d'('fun_app$ah'('swap$d',X3057)) = 'snd$e'(X3057) ),
    inference(variable_rename,[status(thm)],[axiom430]) ).

tcf(c_0_11,plain,
    ! [X62: 'C$',X4: 'A_c_prod$'] :
      ( ( X4 = 'fun_app$p'('fun_app$q'('pair$',esk111_2(X62,X4)),X62) )
      | ( X62 != 'snd$e'(X4) ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

tcf(c_0_12,plain,
    ! [X4: 'A_c_prod$'] : 'fst$d'('fun_app$ah'('swap$d',X4)) = 'snd$e'(X4),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

tff(c_0_13,negated_conjecture,
    'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conjecture9])]) ).

tff(c_0_14,plain,
    ! [X2773: 'A$',X2774: 'C$'] : ( 'fst$e'('fun_app$p'('fun_app$q'('pair$',X2773),X2774)) = X2773 ),
    inference(variable_rename,[status(thm)],[axiom349]) ).

tcf(c_0_15,plain,
    ! [X62: 'C$',X4: 'A_c_prod$'] :
      ( ( X4 = 'fun_app$p'('fun_app$q'('pair$',esk111_2(X62,X4)),X62) )
      | ( X62 != 'fst$d'('fun_app$ah'('swap$d',X4)) ) ),
    inference(rw,[status(thm)],[c_0_11,c_0_12]) ).

tff(c_0_16,negated_conjecture,
    'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
    inference(fof_nnf,[status(thm)],[c_0_13]) ).

tff(c_0_17,plain,
    ! [X1777: 'A_ell2_b_ell2_cblinfun$',X1778: 'C_ell2_d_ell2_cblinfun$',X1779: 'A$',X1780: 'C$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'(X1777,X1778)),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X1779),X1780))) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X1777),'ket$a'(X1779)),'fun_app$u'('cblinfun_apply$b'(X1778),'ket$b'(X1780))) ),
    inference(variable_rename,[status(thm)],[axiom20]) ).

tff(c_0_18,plain,
    ! [X1829: 'C_ell2_d_ell2_cblinfun$',X1830: 'C_ell2_d_ell2_cblinfun$',X1831: 'C_ell2$'] : ( 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a',X1829),X1830)),X1831) = 'plus$i'('fun_app$u'('cblinfun_apply$b'(X1829),X1831),'fun_app$u'('cblinfun_apply$b'(X1830),X1831)) ),
    inference(variable_rename,[status(thm)],[axiom34]) ).

tff(c_0_19,plain,
    ! [X1832: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X1833: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X1834: 'A_c_prod_ell2$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b',X1832),X1833)),X1834) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$',X1832),X1834),'fun_app$k'('fun_app$l'('cblinfun_apply$',X1833),X1834)) ),
    inference(variable_rename,[status(thm)],[axiom35]) ).

tcf(c_0_20,plain,
    ! [X62: 'C$',X10: 'A$'] : 'fst$e'('fun_app$p'('fun_app$q'('pair$',X10),X62)) = X10,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

tcf(c_0_21,plain,
    ! [X4: 'A_c_prod$'] : 'fun_app$p'('fun_app$q'('pair$',esk111_2('fst$d'('fun_app$ah'('swap$d',X4)),X4)),'fst$d'('fun_app$ah'('swap$d',X4))) = X4,
    inference(er,[status(thm)],[c_0_15]) ).

tff(c_0_22,plain,
    ! [X2743: 'A$',X2744: 'C$'] : ( 'snd$e'('fun_app$p'('fun_app$q'('pair$',X2743),X2744)) = X2744 ),
    inference(variable_rename,[status(thm)],[axiom337]) ).

tcf(c_0_23,negated_conjecture,
    'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

tcf(c_0_24,plain,
    ! [X10: 'A$',X13: 'C_ell2_d_ell2_cblinfun$',X59: 'A_ell2_b_ell2_cblinfun$',X62: 'C$'] : 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'(X59,X13)),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X10),X62))) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X59),'ket$a'(X10)),'fun_app$u'('cblinfun_apply$b'(X13),'ket$b'(X62))),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

tcf(c_0_25,plain,
    ! [X13: 'C_ell2_d_ell2_cblinfun$',X14: 'C_ell2_d_ell2_cblinfun$',X113: 'C_ell2$'] : 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a',X13),X14)),X113) = 'plus$i'('fun_app$u'('cblinfun_apply$b'(X13),X113),'fun_app$u'('cblinfun_apply$b'(X14),X113)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

tcf(c_0_26,plain,
    ! [X12: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X11: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X8: 'A_c_prod_ell2$'] : 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b',X11),X12)),X8) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$',X11),X8),'fun_app$k'('fun_app$l'('cblinfun_apply$',X12),X8)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

tcf(c_0_27,plain,
    ! [X4: 'A_c_prod$'] : esk111_2('fst$d'('fun_app$ah'('swap$d',X4)),X4) = 'fst$e'(X4),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

tcf(c_0_28,plain,
    ! [X10: 'A$',X62: 'C$'] : 'snd$e'('fun_app$p'('fun_app$q'('pair$',X10),X62)) = X62,
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

tff(c_0_29,plain,
    ! [X2018: 'B_ell2$',X2019: 'D_ell2$',X2020: 'D_ell2$'] : ( 'tensor_ell2$'(X2018,'plus$i'(X2019,X2020)) = 'plus$u'('tensor_ell2$'(X2018,X2019),'tensor_ell2$'(X2018,X2020)) ),
    inference(variable_rename,[status(thm)],[axiom95]) ).

tcf(c_0_30,negated_conjecture,
    'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).

tcf(c_0_31,plain,
    ! [X10: 'A$',X13: 'C_ell2_d_ell2_cblinfun$',X59: 'A_ell2_b_ell2_cblinfun$',X11: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X62: 'C$'] : 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$',X11),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X10),X62))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X59),'ket$a'(X10)),'fun_app$u'('cblinfun_apply$b'(X13),'ket$b'(X62)))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b',X11),'tensor_op$'(X59,X13))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X10),X62))),
    inference(spm,[status(thm)],[c_0_26,c_0_24]) ).

tcf(c_0_32,plain,
    ! [X59: 'A_ell2_b_ell2_cblinfun$',X13: 'C_ell2_d_ell2_cblinfun$',X4: 'A_c_prod$'] : 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'(X59,X13)),'fun_app$o'('ket$',X4)) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X59),'ket$a'('fst$e'(X4))),'fun_app$u'('cblinfun_apply$b'(X13),'ket$b'('fst$d'('fun_app$ah'('swap$d',X4))))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_27]) ).

tcf(c_0_33,plain,
    ! [X10: 'A$',X62: 'C$'] : 'fst$d'('fun_app$ah'('swap$d','fun_app$p'('fun_app$q'('pair$',X10),X62))) = X62,
    inference(rw,[status(thm)],[c_0_28,c_0_12]) ).

tcf(c_0_34,plain,
    ! [X39: 'D_ell2$',X281: 'B_ell2$',X41: 'D_ell2$'] : 'tensor_ell2$'(X281,'plus$i'(X39,X41)) = 'plus$u'('tensor_ell2$'(X281,X39),'tensor_ell2$'(X281,X41)),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_20]),c_0_33]),c_0_34])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ITP387_1 : TPTP v8.1.2. Released v8.0.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 12:27:55 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.38/0.59  Running first-order model finding
% 0.38/0.59  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.3WvT6lz5jw/E---3.1_20479.p
% 31.12/4.54  # Version: 3.1.0
% 31.12/4.54  # Preprocessing class: FMLMSMSMSSSNFFN.
% 31.12/4.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.12/4.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 31.12/4.54  # Starting new_bool_3 with 300s (1) cores
% 31.12/4.54  # Starting new_bool_1 with 300s (1) cores
% 31.12/4.54  # Starting sh5l with 300s (1) cores
% 31.12/4.54  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 20556 completed with status 0
% 31.12/4.54  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 31.12/4.54  # Preprocessing class: FMLMSMSMSSSNFFN.
% 31.12/4.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.12/4.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 31.12/4.54  # No SInE strategy applied
% 31.12/4.54  # Search class: FGHSM-FSLM31-DFFFFFNN
% 31.12/4.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 31.12/4.54  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 680s (1) cores
% 31.12/4.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 31.12/4.54  # Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 31.12/4.54  # Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 31.12/4.54  # Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 31.12/4.54  # U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 20565 completed with status 0
% 31.12/4.54  # Result found by U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 31.12/4.54  # Preprocessing class: FMLMSMSMSSSNFFN.
% 31.12/4.54  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 31.12/4.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 31.12/4.54  # No SInE strategy applied
% 31.12/4.54  # Search class: FGHSM-FSLM31-DFFFFFNN
% 31.12/4.54  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 31.12/4.54  # Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 680s (1) cores
% 31.12/4.54  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 31.12/4.54  # Starting U----_206c_10_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 31.12/4.54  # Preprocessing time       : 0.011 s
% 31.12/4.54  # Presaturation interreduction done
% 31.12/4.54  
% 31.12/4.54  # Proof found!
% 31.12/4.54  # SZS status Theorem
% 31.12/4.54  # SZS output start CNFRefutation
% See solution above
% 31.12/4.54  # Parsed axioms                        : 1134
% 31.12/4.54  # Removed by relevancy pruning/SinE    : 0
% 31.12/4.54  # Initial clauses                      : 1396
% 31.12/4.54  # Removed in clause preprocessing      : 605
% 31.12/4.54  # Initial clauses in saturation        : 791
% 31.12/4.54  # Processed clauses                    : 19415
% 31.12/4.54  # ...of these trivial                  : 829
% 31.12/4.54  # ...subsumed                          : 14984
% 31.12/4.54  # ...remaining for further processing  : 3602
% 31.12/4.54  # Other redundant clauses eliminated   : 13969
% 31.12/4.54  # Clauses deleted for lack of memory   : 0
% 31.12/4.54  # Backward-subsumed                    : 105
% 31.12/4.54  # Backward-rewritten                   : 166
% 31.12/4.54  # Generated clauses                    : 308922
% 31.12/4.54  # ...of the previous two non-redundant : 279894
% 31.12/4.54  # ...aggressively subsumed             : 0
% 31.12/4.54  # Contextual simplify-reflections      : 0
% 31.12/4.54  # Paramodulations                      : 294748
% 31.12/4.54  # Factorizations                       : 0
% 31.12/4.54  # NegExts                              : 0
% 31.12/4.54  # Equation resolutions                 : 14178
% 31.12/4.54  # Disequality decompositions           : 0
% 31.12/4.54  # Total rewrite steps                  : 158556
% 31.12/4.54  # ...of those cached                   : 135655
% 31.12/4.54  # Propositional unsat checks           : 0
% 31.12/4.54  #    Propositional check models        : 0
% 31.12/4.54  #    Propositional check unsatisfiable : 0
% 31.12/4.54  #    Propositional clauses             : 0
% 31.12/4.54  #    Propositional clauses after purity: 0
% 31.12/4.54  #    Propositional unsat core size     : 0
% 31.12/4.54  #    Propositional preprocessing time  : 0.000
% 31.12/4.54  #    Propositional encoding time       : 0.000
% 31.12/4.54  #    Propositional solver time         : 0.000
% 31.12/4.54  #    Success case prop preproc time    : 0.000
% 31.12/4.54  #    Success case prop encoding time   : 0.000
% 31.12/4.54  #    Success case prop solver time     : 0.000
% 31.12/4.54  # Current number of processed clauses  : 2722
% 31.12/4.54  #    Positive orientable unit clauses  : 357
% 31.12/4.54  #    Positive unorientable unit clauses: 285
% 31.12/4.54  #    Negative unit clauses             : 3
% 31.12/4.54  #    Non-unit-clauses                  : 2077
% 31.12/4.54  # Current number of unprocessed clauses: 260258
% 31.12/4.54  # ...number of literals in the above   : 588283
% 31.12/4.54  # Current number of archived formulas  : 0
% 31.12/4.54  # Current number of archived clauses   : 790
% 31.12/4.54  # Clause-clause subsumption calls (NU) : 2907751
% 31.12/4.54  # Rec. Clause-clause subsumption calls : 2004337
% 31.12/4.54  # Non-unit clause-clause subsumptions  : 13810
% 31.12/4.54  # Unit Clause-clause subsumption calls : 45214
% 31.12/4.54  # Rewrite failures with RHS unbound    : 0
% 31.12/4.54  # BW rewrite match attempts            : 5924
% 31.12/4.54  # BW rewrite match successes           : 3477
% 31.12/4.54  # Condensation attempts                : 0
% 31.12/4.54  # Condensation successes               : 0
% 31.12/4.54  # Termbank termtop insertions          : 5211414
% 31.12/4.54  # Search garbage collected termcells   : 10867
% 31.12/4.54  
% 31.12/4.54  # -------------------------------------------------
% 31.12/4.54  # User time                : 3.712 s
% 31.12/4.54  # System time              : 0.143 s
% 31.12/4.54  # Total time               : 3.855 s
% 31.12/4.54  # Maximum resident set size: 7384 pages
% 31.12/4.54  
% 31.12/4.54  # -------------------------------------------------
% 31.12/4.54  # User time                : 18.531 s
% 31.12/4.54  # System time              : 0.582 s
% 31.12/4.54  # Total time               : 19.112 s
% 31.12/4.54  # Maximum resident set size: 3668 pages
% 31.12/4.54  % E---3.1 exiting
%------------------------------------------------------------------------------