%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP384_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 : Thu Sep 24 12:55:29 PM UTC 2026
% Result : Theorem 0.87s 0.76s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 80 ( 56 equ)
% Maximal formula atoms : 14 ( 1 avg)
% Number of connectives : 60 ( 25 ~; 17 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 21 ( 20 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 15 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
'A_update_b_update_fun_a_update_a_update_fun_fun$': $tType ).
tff(decl_sort2,type,
'B_update_b_update_fun$': $tType ).
tff(decl_sort3,type,
'C_update_b_update_fun$': $tType ).
tff(decl_sort4,type,
'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$': $tType ).
tff(decl_sort5,type,
'B_update_a_update_fun$': $tType ).
tff(decl_sort6,type,
'A_update_b_update_fun$': $tType ).
tff(decl_sort7,type,
'B_update_c_update_fun$': $tType ).
tff(decl_sort8,type,
'C_update_c_update_fun$': $tType ).
tff(decl_sort9,type,
'A_update_set$': $tType ).
tff(decl_sort10,type,
'A_update_a_update_fun$': $tType ).
tff(decl_sort11,type,
'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$': $tType ).
tff(decl_sort12,type,
'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$': $tType ).
tff(decl_sort13,type,
'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$': $tType ).
tff(decl_sort14,type,
'B_update_a_update_fun_b_update_b_update_fun_fun$': $tType ).
tff(decl_sort15,type,
'C_update_a_update_fun$': $tType ).
tff(decl_sort16,type,
'A_update_c_update_fun$': $tType ).
tff(decl_sort17,type,
'B_update_a_update_fun_b_update_c_update_fun_fun$': $tType ).
tff(decl_sort18,type,
'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$': $tType ).
tff(decl_sort19,type,
'C_update_a_update_fun_c_update_b_update_fun_fun$': $tType ).
tff(decl_sort20,type,
'C_update_a_update_fun_c_update_c_update_fun_fun$': $tType ).
tff(decl_55,type,
'fun_app$aj': ( 'B_update_a_update_fun$' * 'B_update_a_update_fun_b_update_b_update_fun_fun$' ) > 'B_update_b_update_fun$' ).
tff(decl_66,type,
'f$': 'B_update_a_update_fun$' ).
tff(decl_73,type,
'id$b': 'A_update_a_update_fun$' ).
tff(decl_92,type,
'fun_app$w': ( 'A_update_c_update_fun$' * 'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$' ) > 'B_update_a_update_fun_b_update_c_update_fun_fun$' ).
tff(decl_112,type,
'comp$ab': ( 'A_update_a_update_fun$' * 'A_update_c_update_fun$' ) > 'A_update_c_update_fun$' ).
tff(decl_125,type,
'fun_app$ak': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$' ) > 'B_update_a_update_fun_b_update_b_update_fun_fun$' ).
tff(decl_127,type,
'comp$k': ( 'A_update_c_update_fun$' * 'C_update_a_update_fun$' ) > 'A_update_a_update_fun$' ).
tff(decl_156,type,
'comp$b': 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' ).
tff(decl_199,type,
'fun_app$ae': ( 'C_update_a_update_fun$' * 'C_update_a_update_fun_c_update_c_update_fun_fun$' ) > 'C_update_c_update_fun$' ).
tff(decl_231,type,
'comp$a': 'A_update_c_update_fun_b_update_a_update_fun_b_update_c_update_fun_fun_fun$' ).
tff(decl_254,type,
'comp$d': 'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$' ).
tff(decl_265,type,
'inv_into$b': ( 'A_update_b_update_fun$' * 'A_update_set$' ) > 'B_update_a_update_fun$' ).
tff(decl_273,type,
'comp$aj': ( 'A_update_b_update_fun$' * 'B_update_c_update_fun$' ) > 'A_update_c_update_fun$' ).
tff(decl_288,type,
'fun_app$x': ( 'C_update_a_update_fun$' * 'C_update_a_update_fun_c_update_b_update_fun_fun$' ) > 'C_update_b_update_fun$' ).
tff(decl_295,type,
'id$': 'C_update_c_update_fun$' ).
tff(decl_306,type,
'id$a': 'B_update_b_update_fun$' ).
tff(decl_325,type,
'register$': 'A_update_c_update_fun$' > $o ).
tff(decl_330,type,
'fun_app$v': ( 'B_update_a_update_fun$' * 'B_update_a_update_fun_b_update_c_update_fun_fun$' ) > 'B_update_c_update_fun$' ).
tff(decl_354,type,
'fun_app$ad': ( 'B_update_a_update_fun$' * 'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$' ) > 'A_update_b_update_fun_a_update_a_update_fun_fun$' ).
tff(decl_356,type,
'fun_app$ac': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun_a_update_a_update_fun_fun$' ) > 'A_update_a_update_fun$' ).
tff(decl_405,type,
'comp$': ( 'C_update_b_update_fun$' * 'B_update_c_update_fun$' ) > 'C_update_c_update_fun$' ).
tff(decl_434,type,
'top$': 'A_update_set$' ).
tff(decl_442,type,
'register$a': 'B_update_a_update_fun$' > $o ).
tff(decl_463,type,
'comp$ae': ( 'C_update_b_update_fun$' * 'B_update_a_update_fun$' ) > 'C_update_a_update_fun$' ).
tff(decl_465,type,
'f$a': 'A_update_b_update_fun$' ).
tff(decl_482,type,
'comp$aa': ( 'C_update_a_update_fun$' * 'A_update_a_update_fun$' ) > 'C_update_a_update_fun$' ).
tff(decl_493,type,
'fun_app$y': ( 'A_update_b_update_fun$' * 'A_update_b_update_fun_c_update_a_update_fun_c_update_b_update_fun_fun_fun$' ) > 'C_update_a_update_fun_c_update_b_update_fun_fun$' ).
tff(decl_498,type,
'inj_on$': ( 'A_update_set$' * 'A_update_b_update_fun$' ) > $o ).
tff(decl_539,type,
'comp$c': 'B_update_a_update_fun_a_update_b_update_fun_a_update_a_update_fun_fun_fun$' ).
tff(decl_552,type,
'g$a': 'C_update_a_update_fun$' ).
tff(decl_580,type,
'comp$e': 'A_update_b_update_fun_b_update_a_update_fun_b_update_b_update_fun_fun_fun$' ).
tff(decl_582,type,
'g$': 'A_update_c_update_fun$' ).
tff(decl_583,type,
'fun_app$af': ( 'A_update_c_update_fun$' * 'A_update_c_update_fun_c_update_a_update_fun_c_update_c_update_fun_fun_fun$' ) > 'C_update_a_update_fun_c_update_c_update_fun_fun$' ).
tff(decl_610,type,
esk1_0: 'B_update_a_update_fun$' ).
tff(decl_611,type,
esk2_0: 'A_update_c_update_fun$' ).
tff(axiom455,axiom,
! [X1377: 'A_update_b_update_fun$',X1378: 'B_update_a_update_fun$'] :
( ( ( 'fun_app$ac'('fun_app$ad'('comp$c',X1378),X1377) = 'id$b' )
& ( 'fun_app$aj'('fun_app$ak'('comp$e',X1377),X1378) = 'id$a' ) )
=> ( 'inv_into$b'('top$',X1377) = X1378 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
tff(conjecture29,conjecture,
'comp$'('fun_app$v'('fun_app$w'('comp$a','g$'),'f$'),'fun_app$x'('fun_app$y'('comp$b','f$a'),'g$a')) = 'id$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture29) ).
tff(axiom575,axiom,
! [X1677: 'A_update_b_update_fun$'] :
( 'inj_on$'(X1677,'top$')
<=> ( 'fun_app$ac'('fun_app$ad'('comp$c','inv_into$b'('top$',X1677)),X1677) = 'id$b' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom575) ).
tff(axiom67,axiom,
'fun_app$aj'('fun_app$ak'('comp$e','f$a'),'f$') = 'id$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
tff(axiom69,axiom,
'fun_app$ac'('fun_app$ad'('comp$c','f$'),'f$a') = 'id$b',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
tff(axiom479,axiom,
! [X1401: 'A_update_b_update_fun$',X1402: 'A_update_c_update_fun$'] :
( 'inj_on$'(X1401,'top$')
=> ( 'comp$aj'('fun_app$v'('fun_app$w'('comp$a',X1402),'inv_into$b'('top$',X1401)),X1401) = X1402 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).
tff(axiom170,axiom,
! [X454: 'A_update_c_update_fun$',X455: 'B_update_a_update_fun$',X456: 'C_update_b_update_fun$'] : ( 'comp$'('fun_app$v'('fun_app$w'('comp$a',X454),X455),X456) = 'fun_app$ae'('fun_app$af'('comp$d',X454),'comp$ae'(X455,X456)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).
tff(axiom187,axiom,
! [X501: 'B_update_c_update_fun$',X2: 'A_update_b_update_fun$',X502: 'C_update_a_update_fun$'] : ( 'comp$'(X501,'fun_app$x'('fun_app$y'('comp$b',X2),X502)) = 'fun_app$ae'('fun_app$af'('comp$d','comp$aj'(X501,X2)),X502) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
tff(axiom179,axiom,
! [X478: 'A_update_c_update_fun$',X479: 'B_update_a_update_fun$',X480: 'A_update_b_update_fun$'] : ( 'comp$ab'(X478,'fun_app$ac'('fun_app$ad'('comp$c',X479),X480)) = 'comp$aj'('fun_app$v'('fun_app$w'('comp$a',X478),X479),X480) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).
tff(axiom186,axiom,
! [X499: 'B_update_a_update_fun$',X2: 'A_update_b_update_fun$',X500: 'C_update_a_update_fun$'] : ( 'comp$ae'(X499,'fun_app$x'('fun_app$y'('comp$b',X2),X500)) = 'comp$aa'('fun_app$ac'('fun_app$ad'('comp$c',X499),X2),X500) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).
tff(axiom66,axiom,
( ! [X108: 'B_update_a_update_fun$',X109: 'A_update_c_update_fun$'] :
( ( ( 'fun_app$ae'('fun_app$af'('comp$d',X109),'g$a') = 'id$' )
& ( 'comp$k'('g$a',X109) = 'id$b' )
& ( 'fun_app$ac'('fun_app$ad'('comp$c',X108),'f$a') = 'id$b' )
& ( 'fun_app$aj'('fun_app$ak'('comp$e','f$a'),X108) = 'id$a' )
& 'register$'(X109)
& 'register$a'(X108) )
=> ~ $true )
=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).
tff(axiom42,axiom,
'fun_app$ae'('fun_app$af'('comp$d','g$'),'g$a') = 'id$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
tff(c_0_12,plain,
! [X2144: 'A_update_b_update_fun$',X2145: 'B_update_a_update_fun$'] :
( ( 'inv_into$b'('top$',X2144) = X2145 )
| ( 'fun_app$ac'('fun_app$ad'('comp$c',X2145),X2144) != 'id$b' )
| ( 'fun_app$aj'('fun_app$ak'('comp$e',X2144),X2145) != 'id$a' ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom455])])]) ).
tff(c_0_13,negated_conjecture,
'comp$'('fun_app$v'('fun_app$w'('comp$a','g$'),'f$'),'fun_app$x'('fun_app$y'('comp$b','f$a'),'g$a')) != 'id$',
inference(assume_negation,[status(cth)],[conjecture29]) ).
tff(c_0_14,plain,
! [X2152: 'A_update_b_update_fun$'] :
( ( 'inj_on$'(X2152,'top$')
| ( 'fun_app$ac'('fun_app$ad'('comp$c','inv_into$b'('top$',X2152)),X2152) != 'id$b' ) )
& ( ( 'fun_app$ac'('fun_app$ad'('comp$c','inv_into$b'('top$',X2152)),X2152) = 'id$b' )
| ~ 'inj_on$'(X2152,'top$') ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom575])])]) ).
tcf(c_0_15,plain,
! [X6: 'B_update_a_update_fun$',X2: 'A_update_b_update_fun$'] :
( ( 'fun_app$ac'('fun_app$ad'('comp$c',X6),X2) != 'id$b' )
| ( 'fun_app$aj'('fun_app$ak'('comp$e',X2),X6) != 'id$a' )
| ( 'inv_into$b'('top$',X2) = X6 ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_16,plain,
'fun_app$aj'('fun_app$ak'('comp$e','f$a'),'f$') = 'id$a',
inference(split_conjunct,[status(thm)],[axiom67]) ).
tcf(c_0_17,plain,
'fun_app$ac'('fun_app$ad'('comp$c','f$'),'f$a') = 'id$b',
inference(split_conjunct,[status(thm)],[axiom69]) ).
tff(c_0_18,negated_conjecture,
'comp$'('fun_app$v'('fun_app$w'('comp$a','g$'),'f$'),'fun_app$x'('fun_app$y'('comp$b','f$a'),'g$a')) != 'id$',
inference(fof_simplification,[status(thm)],[c_0_13]) ).
tff(c_0_19,plain,
! [X1939: 'A_update_b_update_fun$',X1940: 'A_update_c_update_fun$'] :
( ( 'comp$aj'('fun_app$v'('fun_app$w'('comp$a',X1940),'inv_into$b'('top$',X1939)),X1939) = X1940 )
| ~ 'inj_on$'(X1939,'top$') ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom479])])]) ).
tcf(c_0_20,plain,
! [X2: 'A_update_b_update_fun$'] :
( ( 'fun_app$ac'('fun_app$ad'('comp$c','inv_into$b'('top$',X2)),X2) != 'id$b' )
| 'inj_on$'(X2,'top$') ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_21,plain,
'inv_into$b'('top$','f$a') = 'f$',
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
tff(c_0_22,negated_conjecture,
'comp$'('fun_app$v'('fun_app$w'('comp$a','g$'),'f$'),'fun_app$x'('fun_app$y'('comp$b','f$a'),'g$a')) != 'id$',
inference(fof_nnf,[status(thm)],[c_0_18]) ).
tff(c_0_23,plain,
! [X1895: 'A_update_c_update_fun$',X1896: 'B_update_a_update_fun$',X1897: 'C_update_b_update_fun$'] : ( 'comp$'('fun_app$v'('fun_app$w'('comp$a',X1895),X1896),X1897) = 'fun_app$ae'('fun_app$af'('comp$d',X1895),'comp$ae'(X1896,X1897)) ),
inference(variable_rename,[status(thm)],[axiom170]) ).
tff(c_0_24,plain,
! [X1898: 'B_update_c_update_fun$',X1899: 'A_update_b_update_fun$',X1900: 'C_update_a_update_fun$'] : ( 'comp$'(X1898,'fun_app$x'('fun_app$y'('comp$b',X1899),X1900)) = 'fun_app$ae'('fun_app$af'('comp$d','comp$aj'(X1898,X1899)),X1900) ),
inference(variable_rename,[status(thm)],[axiom187]) ).
tff(c_0_25,plain,
! [X1936: 'A_update_c_update_fun$',X1937: 'B_update_a_update_fun$',X1938: 'A_update_b_update_fun$'] : ( 'comp$ab'(X1936,'fun_app$ac'('fun_app$ad'('comp$c',X1937),X1938)) = 'comp$aj'('fun_app$v'('fun_app$w'('comp$a',X1936),X1937),X1938) ),
inference(variable_rename,[status(thm)],[axiom179]) ).
tff(c_0_26,plain,
! [X1930: 'B_update_a_update_fun$',X1931: 'A_update_b_update_fun$',X1932: 'C_update_a_update_fun$'] : ( 'comp$ae'(X1930,'fun_app$x'('fun_app$y'('comp$b',X1931),X1932)) = 'comp$aa'('fun_app$ac'('fun_app$ad'('comp$c',X1930),X1931),X1932) ),
inference(variable_rename,[status(thm)],[axiom186]) ).
tff(c_0_27,plain,
( ( ~ $true
| $true )
& ( ~ $true
| ( 'fun_app$ae'('fun_app$af'('comp$d',esk2_0),'g$a') = 'id$' ) )
& ( ~ $true
| ( 'comp$k'('g$a',esk2_0) = 'id$b' ) )
& ( ~ $true
| ( 'fun_app$ac'('fun_app$ad'('comp$c',esk1_0),'f$a') = 'id$b' ) )
& ( ~ $true
| ( 'fun_app$aj'('fun_app$ak'('comp$e','f$a'),esk1_0) = 'id$a' ) )
& ( ~ $true
| 'register$'(esk2_0) )
& ( ~ $true
| 'register$a'(esk1_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom66])])])])]) ).
tcf(c_0_28,plain,
! [X11: 'A_update_c_update_fun$',X2: 'A_update_b_update_fun$'] :
( ~ 'inj_on$'(X2,'top$')
| ( 'comp$aj'('fun_app$v'('fun_app$w'('comp$a',X11),'inv_into$b'('top$',X2)),X2) = X11 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
tcf(c_0_29,plain,
'inj_on$'('f$a','top$'),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_17])]) ).
tcf(c_0_30,negated_conjecture,
'comp$'('fun_app$v'('fun_app$w'('comp$a','g$'),'f$'),'fun_app$x'('fun_app$y'('comp$b','f$a'),'g$a')) != 'id$',
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tcf(c_0_31,plain,
! [X6: 'B_update_a_update_fun$',X11: 'A_update_c_update_fun$',X86: 'C_update_b_update_fun$'] : 'comp$'('fun_app$v'('fun_app$w'('comp$a',X11),X6),X86) = 'fun_app$ae'('fun_app$af'('comp$d',X11),'comp$ae'(X6,X86)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
tcf(c_0_32,plain,
! [X2: 'A_update_b_update_fun$',X82: 'B_update_c_update_fun$',X4: 'C_update_a_update_fun$'] : 'comp$'(X82,'fun_app$x'('fun_app$y'('comp$b',X2),X4)) = 'fun_app$ae'('fun_app$af'('comp$d','comp$aj'(X82,X2)),X4),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tcf(c_0_33,plain,
! [X11: 'A_update_c_update_fun$',X6: 'B_update_a_update_fun$',X2: 'A_update_b_update_fun$'] : 'comp$ab'(X11,'fun_app$ac'('fun_app$ad'('comp$c',X6),X2)) = 'comp$aj'('fun_app$v'('fun_app$w'('comp$a',X11),X6),X2),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_34,plain,
! [X2: 'A_update_b_update_fun$',X6: 'B_update_a_update_fun$',X4: 'C_update_a_update_fun$'] : 'comp$ae'(X6,'fun_app$x'('fun_app$y'('comp$b',X2),X4)) = 'comp$aa'('fun_app$ac'('fun_app$ad'('comp$c',X6),X2),X4),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
tcf(c_0_35,plain,
( ~ $true
| ( 'fun_app$ac'('fun_app$ad'('comp$c',esk1_0),'f$a') = 'id$b' ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
tcf(c_0_36,plain,
! [X11: 'A_update_c_update_fun$'] : 'comp$aj'('fun_app$v'('fun_app$w'('comp$a',X11),'f$'),'f$a') = X11,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_21]),c_0_29])]) ).
tcf(c_0_37,negated_conjecture,
'fun_app$ae'('fun_app$af'('comp$d','g$'),'comp$ae'('f$','fun_app$x'('fun_app$y'('comp$b','f$a'),'g$a'))) != 'id$',
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
tcf(c_0_38,plain,
! [X2: 'A_update_b_update_fun$',X11: 'A_update_c_update_fun$',X6: 'B_update_a_update_fun$',X4: 'C_update_a_update_fun$'] : 'fun_app$ae'('fun_app$af'('comp$d',X11),'comp$aa'('fun_app$ac'('fun_app$ad'('comp$c',X6),X2),X4)) = 'fun_app$ae'('fun_app$af'('comp$d','comp$ab'(X11,'fun_app$ac'('fun_app$ad'('comp$c',X6),X2))),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]) ).
tcf(c_0_39,plain,
'fun_app$ac'('fun_app$ad'('comp$c',esk1_0),'f$a') = 'id$b',
inference(cn,[status(thm)],[c_0_35]) ).
tcf(c_0_40,plain,
! [X11: 'A_update_c_update_fun$'] : 'comp$ab'(X11,'id$b') = X11,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_33]),c_0_17]) ).
tcf(c_0_41,negated_conjecture,
'fun_app$ae'('fun_app$af'('comp$d','g$'),'comp$aa'('id$b','g$a')) != 'id$',
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_34]),c_0_17]) ).
tcf(c_0_42,plain,
! [X11: 'A_update_c_update_fun$',X4: 'C_update_a_update_fun$'] : 'fun_app$ae'('fun_app$af'('comp$d',X11),'comp$aa'('id$b',X4)) = 'fun_app$ae'('fun_app$af'('comp$d',X11),X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
tcf(c_0_43,plain,
'fun_app$ae'('fun_app$af'('comp$d','g$'),'g$a') = 'id$',
inference(split_conjunct,[status(thm)],[axiom42]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP384_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.38 % Computer : n011.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Sun Sep 20 22:36:10 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.87/0.76 % Version: 3.5.1
% 0.87/0.76 % partial match(1): FMLMSMSMSSSNFFN
% 0.87/0.76 % Preprocessing class: FMLMSMMMSSSNFFN.
% 0.87/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.87/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.87/0.76 % Starting new_bool_3 with 300s (1) cores
% 0.87/0.76 % Starting new_bool_1 with 300s (1) cores
% 0.87/0.76 % Starting sh5l with 300s (1) cores
% 0.87/0.76 % new_bool_3 with pid 336729 completed with status 0
% 0.87/0.76 % Result found by new_bool_3
% 0.87/0.76 % partial match(1): FMLMSMSMSSSNFFN
% 0.87/0.76 % Preprocessing class: FMLMSMMMSSSNFFN.
% 0.87/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.87/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.87/0.76 % Starting new_bool_3 with 300s (1) cores
% 0.87/0.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.87/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.87/0.76 % Search class: FHUSM-FFLM21-MFFFFFNN
% 0.87/0.76 % partial match(2): FHUSM-FFSF21-MFFFFFNN
% 0.87/0.76 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.87/0.76 % Starting SubtermCWHack with 28s (1) cores
% 0.87/0.76 % SubtermCWHack with pid 336732 completed with status 0
% 0.87/0.76 % Result found by SubtermCWHack
% 0.87/0.76 % partial match(1): FMLMSMSMSSSNFFN
% 0.87/0.76 % Preprocessing class: FMLMSMMMSSSNFFN.
% 0.87/0.76 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.87/0.76 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.87/0.76 % Starting new_bool_3 with 300s (1) cores
% 0.87/0.76 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.87/0.76 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.87/0.76 % Search class: FHUSM-FFLM21-MFFFFFNN
% 0.87/0.76 % partial match(2): FHUSM-FFSF21-MFFFFFNN
% 0.87/0.76 % Scheduled 11 strats onto 1 cores with 300 seconds (300 total)
% 0.87/0.76 % Starting SubtermCWHack with 28s (1) cores
% 0.87/0.76 % Preprocessing time : 0.005 s
% 0.87/0.76
% 0.87/0.76 % Proof found!
% 0.87/0.76 % SZS status Theorem
% 0.87/0.76 % SZS output start CNFRefutation
% See solution above
% 0.87/0.76 % Parsed axioms : 1470
% 0.87/0.76 % Removed by relevancy pruning/SinE : 1346
% 0.87/0.76 % Initial clauses : 160
% 0.87/0.76 % Removed in clause preprocessing : 6
% 0.87/0.76 % Initial clauses in saturation : 154
% 0.87/0.76 % Processed clauses : 2003
% 0.87/0.76 % ...of these trivial : 49
% 0.87/0.76 % ...subsumed : 1336
% 0.87/0.76 % ...remaining for further processing : 618
% 0.87/0.76 % Other redundant clauses eliminated : 72
% 0.87/0.76 % Clauses deleted for lack of memory : 0
% 0.87/0.76 % Backward-subsumed : 15
% 0.87/0.76 % Backward-rewritten : 60
% 0.87/0.76 % Generated clauses : 7429
% 0.87/0.76 % ...of the previous two non-redundant : 6558
% 0.87/0.76 % ...aggressively subsumed : 0
% 0.87/0.76 % Contextual simplify-reflections : 155
% 0.87/0.76 % Paramodulations : 7353
% 0.87/0.76 % Factorizations : 0
% 0.87/0.76 % NegExts : 0
% 0.87/0.76 % Equation resolutions : 76
% 0.87/0.76 % Disequality decompositions : 0
% 0.87/0.76 % Total rewrite steps : 3003
% 0.87/0.76 % ...of those cached : 2820
% 0.87/0.76 % Propositional unsat checks : 0
% 0.87/0.76 % Propositional check models : 0
% 0.87/0.76 % Propositional check unsatisfiable : 0
% 0.87/0.76 % Propositional clauses : 0
% 0.87/0.76 % Propositional clauses after purity: 0
% 0.87/0.76 % Propositional unsat core size : 0
% 0.87/0.76 % Propositional preprocessing time : 0.000
% 0.87/0.76 % Propositional encoding time : 0.000
% 0.87/0.76 % Propositional solver time : 0.000
% 0.87/0.76 % Success case prop preproc time : 0.000
% 0.87/0.76 % Success case prop encoding time : 0.000
% 0.87/0.76 % Success case prop solver time : 0.000
% 0.87/0.76 % Current number of processed clauses : 532
% 0.87/0.76 % Positive orientable unit clauses : 78
% 0.87/0.76 % Positive unorientable unit clauses: 0
% 0.87/0.76 % Negative unit clauses : 0
% 0.87/0.76 % Non-unit-clauses : 454
% 0.87/0.76 % Current number of unprocessed clauses: 4472
% 0.87/0.76 % ...number of literals in the above : 14646
% 0.87/0.76 % Current number of archived formulas : 0
% 0.87/0.76 % Current number of archived clauses : 75
% 0.87/0.76 % Clause-clause subsumption calls (NU) : 40011
% 0.87/0.76 % Rec. Clause-clause subsumption calls : 37110
% 0.87/0.76 % Non-unit clause-clause subsumptions : 1506
% 0.87/0.76 % Unit Clause-clause subsumption calls : 371
% 0.87/0.76 % Rewrite failures with RHS unbound : 0
% 0.87/0.76 % BW rewrite match attempts : 26
% 0.87/0.76 % BW rewrite match successes : 24
% 0.87/0.76 % Condensation attempts : 0
% 0.87/0.76 % Condensation successes : 0
% 0.87/0.76 % Termbank termtop insertions : 132698
% 0.87/0.76 % Search garbage collected termcells : 9037
% 0.87/0.76
% 0.87/0.76 % -------------------------------------------------
% 0.87/0.76 % User time : 0.218 s
% 0.87/0.76 % System time : 0.021 s
% 0.87/0.76 % Total time : 0.239 s
% 0.87/0.76 % Maximum resident set size: 6944 pages
% 0.87/0.76
% 0.87/0.76 % -------------------------------------------------
% 0.87/0.76 % User time : 0.266 s
% 0.87/0.76 % System time : 0.029 s
% 0.87/0.76 % Total time : 0.295 s
% 0.87/0.76 % Maximum resident set size: 7168 pages
% 0.87/0.76 % E exiting
%------------------------------------------------------------------------------