%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ITP020^2 : 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 : n002.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 08:05:16 AM UTC 2026
% Result : Theorem 21.95s 3.48s
% Output : CNFRefutation 21.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 0 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 722 ( 39 ~; 35 |; 9 &; 634 @)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 12 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 55 ( 0 ^; 50 !; 5 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
del: $tType ).
thf(decl_23,type,
bool: del ).
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_29,type,
p: $i > $o ).
thf(decl_39,type,
c_2Epred__set_2EUNIV: del > $i ).
thf(decl_40,type,
ty_2Epair_2Eprod: del > del > del ).
thf(decl_41,type,
c_2Epred__set_2ECROSS: del > del > $i ).
thf(decl_42,type,
c_2Epred__set_2EBIJ: del > del > $i ).
thf(decl_43,type,
ty_2Enum_2Enum: del ).
thf(decl_79,type,
esk27_4: del > del > $i > $i > $i ).
thf(decl_80,type,
esk28_4: del > del > $i > $i > $i ).
thf(decl_81,type,
esk29_0: $i ).
thf(conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV,conjecture,
? [X51: $i] :
( ( mem @ X51 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X51 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yBb18OyTvw/E---3.1_1741323.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).
thf(conj_thm_2Epred__set_2EBIJ__SYM,axiom,
! [X15: del,X19: del,X44: $i] :
( ( mem @ X44 @ ( arr @ X15 @ bool ) )
=> ! [X45: $i] :
( ( mem @ X45 @ ( arr @ X19 @ bool ) )
=> ( ? [X46: $i] :
( ( mem @ X46 @ ( arr @ X15 @ X19 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X15 @ X19 ) @ X46 ) @ X44 ) @ X45 ) ) )
<=> ? [X47: $i] :
( ( mem @ X47 @ ( arr @ X19 @ X15 ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X19 @ X15 ) @ X47 ) @ X45 ) @ X44 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yBb18OyTvw/E---3.1_1741323.p',conj_thm_2Epred__set_2EBIJ__SYM) ).
thf(conj_thm_2Eutil__prob_2ENUM__2D__BIJ,axiom,
? [X51: $i] :
( ( mem @ X51 @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ X51 ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yBb18OyTvw/E---3.1_1741323.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ) ).
thf(mem_c_2Epred__set_2EUNIV,axiom,
! [X15: del] : ( mem @ ( c_2Epred__set_2EUNIV @ X15 ) @ ( arr @ X15 @ bool ) ),
file('/export/starexec/sandbox/tmp/tmp.yBb18OyTvw/E---3.1_1741323.p',mem_c_2Epred__set_2EUNIV) ).
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.yBb18OyTvw/E---3.1_1741323.p',ap_tp) ).
thf(mem_c_2Epred__set_2ECROSS,axiom,
! [X15: del,X19: del] : ( mem @ ( c_2Epred__set_2ECROSS @ X15 @ X19 ) @ ( arr @ ( arr @ X15 @ bool ) @ ( arr @ ( arr @ X19 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X15 @ X19 ) @ bool ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.yBb18OyTvw/E---3.1_1741323.p',mem_c_2Epred__set_2ECROSS) ).
thf(c_0_6,negated_conjecture,
~ ? [X51: $i] :
( ( mem @ X51 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X51 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV]) ).
thf(c_0_7,plain,
! [X328: del,X329: del,X330: $i,X331: $i,X332: $i,X334: $i] :
( ( ( mem @ ( esk27_4 @ X328 @ X329 @ X330 @ X331 ) @ ( arr @ X329 @ X328 ) )
| ~ ( mem @ X332 @ ( arr @ X328 @ X329 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X328 @ X329 ) @ X332 ) @ X330 ) @ X331 ) )
| ~ ( mem @ X331 @ ( arr @ X329 @ bool ) )
| ~ ( mem @ X330 @ ( arr @ X328 @ bool ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X329 @ X328 ) @ ( esk27_4 @ X328 @ X329 @ X330 @ X331 ) ) @ X331 ) @ X330 ) )
| ~ ( mem @ X332 @ ( arr @ X328 @ X329 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X328 @ X329 ) @ X332 ) @ X330 ) @ X331 ) )
| ~ ( mem @ X331 @ ( arr @ X329 @ bool ) )
| ~ ( mem @ X330 @ ( arr @ X328 @ bool ) ) )
& ( ( mem @ ( esk28_4 @ X328 @ X329 @ X330 @ X331 ) @ ( arr @ X328 @ X329 ) )
| ~ ( mem @ X334 @ ( arr @ X329 @ X328 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X329 @ X328 ) @ X334 ) @ X331 ) @ X330 ) )
| ~ ( mem @ X331 @ ( arr @ X329 @ bool ) )
| ~ ( mem @ X330 @ ( arr @ X328 @ bool ) ) )
& ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X328 @ X329 ) @ ( esk28_4 @ X328 @ X329 @ X330 @ X331 ) ) @ X330 ) @ X331 ) )
| ~ ( mem @ X334 @ ( arr @ X329 @ X328 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X329 @ X328 ) @ X334 ) @ X331 ) @ X330 ) )
| ~ ( mem @ X331 @ ( arr @ X329 @ bool ) )
| ~ ( mem @ X330 @ ( arr @ X328 @ bool ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2EBIJ__SYM])])])])])]) ).
thf(c_0_8,plain,
( ( mem @ esk29_0 @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ esk29_0 ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[conj_thm_2Eutil__prob_2ENUM__2D__BIJ])]) ).
thf(c_0_9,plain,
! [X228: del] : ( mem @ ( c_2Epred__set_2EUNIV @ X228 ) @ ( arr @ X228 @ bool ) ),
inference(variable_rename,[status(thm)],[mem_c_2Epred__set_2EUNIV]) ).
thf(c_0_10,plain,
! [X196: del,X197: del,X198: $i,X199: $i] :
( ~ ( mem @ X198 @ ( arr @ X196 @ X197 ) )
| ~ ( mem @ X199 @ X196 )
| ( mem @ ( ap @ X198 @ X199 ) @ X197 ) ),
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_11,plain,
! [X229: del,X230: del] : ( mem @ ( c_2Epred__set_2ECROSS @ X229 @ X230 ) @ ( arr @ ( arr @ X229 @ bool ) @ ( arr @ ( arr @ X230 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X229 @ X230 ) @ bool ) ) ) ),
inference(variable_rename,[status(thm)],[mem_c_2Epred__set_2ECROSS]) ).
thf(c_0_12,negated_conjecture,
! [X357: $i] :
( ~ ( mem @ X357 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X357 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
thf(c_0_13,plain,
! [X2: $i,X3: del,X6: $i,X5: $i,X4: del] :
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X3 @ X4 ) @ ( esk27_4 @ X4 @ X3 @ X2 @ X5 ) ) @ X5 ) @ X2 ) )
| ~ ( mem @ X6 @ ( arr @ X4 @ X3 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X4 @ X3 ) @ X6 ) @ X2 ) @ X5 ) )
| ~ ( mem @ X5 @ ( arr @ X3 @ bool ) )
| ~ ( mem @ X2 @ ( arr @ X4 @ bool ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_14,plain,
p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ esk29_0 ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_15,plain,
! [X3: del] : ( mem @ ( c_2Epred__set_2EUNIV @ X3 ) @ ( arr @ X3 @ bool ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
thf(c_0_16,plain,
mem @ esk29_0 @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
thf(c_0_17,plain,
! [X2: $i,X6: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( esk27_4 @ X3 @ X4 @ X2 @ X5 ) @ ( arr @ X4 @ X3 ) )
| ~ ( mem @ X6 @ ( arr @ X3 @ X4 ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X3 @ X4 ) @ X6 ) @ X2 ) @ X5 ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ bool ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_18,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_10]) ).
thf(c_0_19,plain,
! [X3: del,X4: del] : ( mem @ ( c_2Epred__set_2ECROSS @ X3 @ X4 ) @ ( arr @ ( arr @ X3 @ bool ) @ ( arr @ ( arr @ X4 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X3 @ X4 ) @ bool ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_20,negated_conjecture,
! [X2: $i] :
( ~ ( mem @ X2 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
| ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X2 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_21,plain,
( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( esk27_4 @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) )
| ~ ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
thf(c_0_22,plain,
( ( mem @ ( esk27_4 @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
| ~ ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]),c_0_16])]) ).
thf(c_0_23,plain,
! [X2: $i,X4: del,X3: del] :
( ( mem @ ( ap @ ( c_2Epred__set_2ECROSS @ X3 @ X4 ) @ X2 ) @ ( arr @ ( arr @ X4 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X3 @ X4 ) @ bool ) ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
thf(c_0_24,negated_conjecture,
~ ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_25,plain,
! [X2: $i,X5: $i,X4: del,X3: del] :
( ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ X3 @ X4 ) @ X2 ) @ X5 ) @ ( arr @ ( ty_2Epair_2Eprod @ X3 @ X4 ) @ bool ) )
| ~ ( mem @ X5 @ ( arr @ X4 @ bool ) )
| ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
thf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP020^2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.15 % Computer : n002.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Sep 29 19:36:22 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 Running higher-order theorem proving
% 0.10/0.20 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.yBb18OyTvw/E---3.1_1741323.p
% 21.95/3.48 % Version: 3.5.1-ho
% 21.95/3.48 % Preprocessing class: HSLSSMSMSSSNSFA.
% 21.95/3.48 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 21.95/3.48 % Starting new_ho_10 with 900s (3) cores
% 21.95/3.48 % Starting sh2lt with 300s (1) cores
% 21.95/3.48 % Starting new_ho_5 with 300s (1) cores
% 21.95/3.48 % Starting full_lambda_5 with 300s (1) cores
% 21.95/3.48 % Starting sh9 with 300s (1) cores
% 21.95/3.48 % Starting ehoh_best8_lambda with 300s (1) cores
% 21.95/3.48 % new_ho_10 with pid 1741336 completed with status 0
% 21.95/3.48 % Result found by new_ho_10
% 21.95/3.48 % Preprocessing class: HSLSSMSMSSSNSFA.
% 21.95/3.48 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 21.95/3.48 % Starting new_ho_10 with 900s (3) cores
% 21.95/3.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 21.95/3.48 % No SInE strategy applied
% 21.95/3.48 % Search class: HGHSM-FSLM32-MSFFFFBN
% 21.95/3.48 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 21.95/3.48 % Starting SubtermCWHack with 82s (1) cores
% 21.95/3.48 % Starting new_ho_10 with 91s (1) cores
% 21.95/3.48 % Starting sh5l with 82s (1) cores
% 21.95/3.48 % new_ho_10 with pid 1741343 completed with status 0
% 21.95/3.48 % Result found by new_ho_10
% 21.95/3.48 % Preprocessing class: HSLSSMSMSSSNSFA.
% 21.95/3.48 % Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 21.95/3.48 % Starting new_ho_10 with 900s (3) cores
% 21.95/3.48 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 21.95/3.48 % No SInE strategy applied
% 21.95/3.48 % Search class: HGHSM-FSLM32-MSFFFFBN
% 21.95/3.48 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 21.95/3.48 % Starting SubtermCWHack with 82s (1) cores
% 21.95/3.48 % Starting new_ho_10 with 91s (1) cores
% 21.95/3.48 % Preprocessing time : 0.006 s
% 21.95/3.48 % Presaturation interreduction done
% 21.95/3.48
% 21.95/3.48 % Proof found!
% 21.95/3.48 % SZS status Theorem
% 21.95/3.48 % SZS output start CNFRefutation
% See solution above
% 21.95/3.48 % Parsed axioms : 95
% 21.95/3.48 % Removed by relevancy pruning/SinE : 0
% 21.95/3.48 % Initial clauses : 424
% 21.95/3.48 % Removed in clause preprocessing : 291
% 21.95/3.48 % Initial clauses in saturation : 133
% 21.95/3.48 % Processed clauses : 1940
% 21.95/3.48 % ...of these trivial : 11
% 21.95/3.48 % ...subsumed : 432
% 21.95/3.48 % ...remaining for further processing : 1497
% 21.95/3.48 % Other redundant clauses eliminated : 1
% 21.95/3.48 % Clauses deleted for lack of memory : 0
% 21.95/3.48 % Backward-subsumed : 19
% 21.95/3.48 % Backward-rewritten : 38
% 21.95/3.48 % Generated clauses : 63378
% 21.95/3.48 % ...of the previous two non-redundant : 62147
% 21.95/3.48 % ...aggressively subsumed : 0
% 21.95/3.48 % Contextual simplify-reflections : 19
% 21.95/3.48 % Paramodulations : 63361
% 21.95/3.48 % Factorizations : 13
% 21.95/3.48 % NegExts : 0
% 21.95/3.48 % Equation resolutions : 2
% 21.95/3.48 % Disequality decompositions : 0
% 21.95/3.48 % Total rewrite steps : 13094
% 21.95/3.48 % ...of those cached : 13060
% 21.95/3.48 % Propositional unsat checks : 0
% 21.95/3.48 % Propositional check models : 0
% 21.95/3.48 % Propositional check unsatisfiable : 0
% 21.95/3.48 % Propositional clauses : 0
% 21.95/3.48 % Propositional clauses after purity: 0
% 21.95/3.48 % Propositional unsat core size : 0
% 21.95/3.48 % Propositional preprocessing time : 0.000
% 21.95/3.48 % Propositional encoding time : 0.000
% 21.95/3.48 % Propositional solver time : 0.000
% 21.95/3.48 % Success case prop preproc time : 0.000
% 21.95/3.48 % Success case prop encoding time : 0.000
% 21.95/3.48 % Success case prop solver time : 0.000
% 21.95/3.48 % Current number of processed clauses : 1322
% 21.95/3.48 % Positive orientable unit clauses : 43
% 21.95/3.48 % Positive unorientable unit clauses: 0
% 21.95/3.48 % Negative unit clauses : 3
% 21.95/3.48 % Non-unit-clauses : 1276
% 21.95/3.48 % Current number of unprocessed clauses: 60201
% 21.95/3.48 % ...number of literals in the above : 471813
% 21.95/3.48 % Current number of archived formulas : 0
% 21.95/3.48 % Current number of archived clauses : 174
% 21.95/3.48 % Clause-clause subsumption calls (NU) : 279216
% 21.95/3.48 % Rec. Clause-clause subsumption calls : 21597
% 21.95/3.48 % Non-unit clause-clause subsumptions : 273
% 21.95/3.48 % Unit Clause-clause subsumption calls : 4196
% 21.95/3.48 % Rewrite failures with RHS unbound : 0
% 21.95/3.48 % BW rewrite match attempts : 34
% 21.95/3.48 % BW rewrite match successes : 21
% 21.95/3.48 % Condensation attempts : 1940
% 21.95/3.48 % Condensation successes : 0
% 21.95/3.48 % Termbank termtop insertions : 2409014
% 21.95/3.48 % Search garbage collected termcells : 6062
% 21.95/3.48
% 21.95/3.48 % -------------------------------------------------
% 21.95/3.48 % User time : 2.996 s
% 21.95/3.48 % System time : 0.081 s
% 21.95/3.48 % Total time : 3.077 s
% 21.95/3.48 % Maximum resident set size: 4808 pages
% 21.95/3.48
% 21.95/3.48 % -------------------------------------------------
% 21.95/3.48 % User time : 8.973 s
% 21.95/3.48 % System time : 0.258 s
% 21.95/3.48 % Total time : 9.231 s
% 21.95/3.48 % Maximum resident set size: 4864 pages
% 21.95/3.48 % E exiting
%------------------------------------------------------------------------------