%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW477+7 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 03:10:55 PM UTC 2026
% Result : Theorem 24.09s 10.10s
% Output : CNFRefutation 24.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 15 unt; 0 def)
% Number of atoms : 100 ( 56 equ)
% Maximal formula atoms : 58 ( 4 avg)
% Number of connectives : 110 ( 33 ~; 55 |; 20 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 14 con; 0-4 aty)
% Number of variables : 37 ( 1 sgn 21 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_1__096_B_BT_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_061_061_062_AEX,axiom,
! [X10] :
( hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),ha),e),ea),X10))
=> ? [X11] :
( hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(ty,fun(ty,bool)),widen(product_prod(list(list(char)),exp(list(char)))),p),X11),X10))
& hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__096_B_BT_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_061_061_062_AEX) ).
fof(fact_579_ty_Osimps_I20_J,axiom,
! [X129] : nt != hAPP(list(char),ty,class,X129),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_ty_Osimps_I20_J) ).
fof(fact_606_widen_Osimps,axiom,
! [X1,X15,X223,X224] :
( hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X1)))))))),fun(ty,fun(ty,bool)),widen(X1),X15),X223),X224))
<=> ( ? [X216] :
( X224 = hAPP(list(char),ty,class,X216)
& X223 = nt )
| ? [X216,X220] :
( hBOOL(hAPP(fun(product_prod(list(char),list(char)),bool),bool,hAPP(product_prod(list(char),list(char)),fun(fun(product_prod(list(char),list(char)),bool),bool),member(product_prod(list(char),list(char))),hAPP(list(char),product_prod(list(char),list(char)),hAPP(list(char),fun(list(char),product_prod(list(char),list(char))),product_Pair(list(char),list(char)),X216),X220)),hAPP(fun(product_prod(list(char),list(char)),bool),fun(product_prod(list(char),list(char)),bool),transitive_rtrancl(list(char)),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X1)))))))),fun(product_prod(list(char),list(char)),bool),subcls1(X1),X15))))
& X224 = hAPP(list(char),ty,class,X220)
& X223 = hAPP(list(char),ty,class,X216) )
| ? [X99] :
( X224 = X99
& X223 = X99 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_widen_Osimps) ).
fof(fact_0__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096,axiom,
hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),ha),e),ea),nt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096) ).
fof(conj_0,conjecture,
hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),nt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(c_0_5,plain,
! [X636] :
( ( ~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),ha),e),ea),X636))
| hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(ty,fun(ty,bool)),widen(product_prod(list(list(char)),exp(list(char)))),p),esk62_1(X636)),X636)) )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),ha),e),ea),X636))
| hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),esk62_1(X636))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_1__096_B_BT_O_AP_ME_Mh_A_092_060turnstile_062_Ae_A_058_AT_A_061_061_062_AEX])])])])]) ).
fof(c_0_6,plain,
! [X129] : nt != hAPP(list(char),ty,class,X129),
inference(fof_simplification,[status(thm)],[fact_579_ty_Osimps_I20_J]) ).
fof(c_0_7,plain,
! [X344,X345,X346,X347,X352,X353,X354,X355,X356,X357,X358,X359] :
( ( hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X352)))))))),fun(ty,fun(ty,bool)),widen(X352),X353),X354),X355))
| X355 != hAPP(list(char),ty,class,X359)
| X354 != nt )
& ( hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X352)))))))),fun(ty,fun(ty,bool)),widen(X352),X353),X354),X355))
| ~ hBOOL(hAPP(fun(product_prod(list(char),list(char)),bool),bool,hAPP(product_prod(list(char),list(char)),fun(fun(product_prod(list(char),list(char)),bool),bool),member(product_prod(list(char),list(char))),hAPP(list(char),product_prod(list(char),list(char)),hAPP(list(char),fun(list(char),product_prod(list(char),list(char))),product_Pair(list(char),list(char)),X357),X358)),hAPP(fun(product_prod(list(char),list(char)),bool),fun(product_prod(list(char),list(char)),bool),transitive_rtrancl(list(char)),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X352)))))))),fun(product_prod(list(char),list(char)),bool),subcls1(X352),X353))))
| X355 != hAPP(list(char),ty,class,X358)
| X354 != hAPP(list(char),ty,class,X357) )
& ( hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X352)))))))),fun(ty,fun(ty,bool)),widen(X352),X353),X354),X355))
| X355 != X356
| X354 != X356 )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X347 = esk2_4(X344,X345,X346,X347)
| hBOOL(hAPP(fun(product_prod(list(char),list(char)),bool),bool,hAPP(product_prod(list(char),list(char)),fun(fun(product_prod(list(char),list(char)),bool),bool),member(product_prod(list(char),list(char))),hAPP(list(char),product_prod(list(char),list(char)),hAPP(list(char),fun(list(char),product_prod(list(char),list(char))),product_Pair(list(char),list(char)),esk3_4(X344,X345,X346,X347)),esk4_4(X344,X345,X346,X347))),hAPP(fun(product_prod(list(char),list(char)),bool),fun(product_prod(list(char),list(char)),bool),transitive_rtrancl(list(char)),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(product_prod(list(char),list(char)),bool),subcls1(X344),X345))))
| X347 = hAPP(list(char),ty,class,esk5_4(X344,X345,X346,X347)) )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X347 = esk2_4(X344,X345,X346,X347)
| hBOOL(hAPP(fun(product_prod(list(char),list(char)),bool),bool,hAPP(product_prod(list(char),list(char)),fun(fun(product_prod(list(char),list(char)),bool),bool),member(product_prod(list(char),list(char))),hAPP(list(char),product_prod(list(char),list(char)),hAPP(list(char),fun(list(char),product_prod(list(char),list(char))),product_Pair(list(char),list(char)),esk3_4(X344,X345,X346,X347)),esk4_4(X344,X345,X346,X347))),hAPP(fun(product_prod(list(char),list(char)),bool),fun(product_prod(list(char),list(char)),bool),transitive_rtrancl(list(char)),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(product_prod(list(char),list(char)),bool),subcls1(X344),X345))))
| X346 = nt )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X347 = esk2_4(X344,X345,X346,X347)
| X347 = hAPP(list(char),ty,class,esk4_4(X344,X345,X346,X347))
| X347 = hAPP(list(char),ty,class,esk5_4(X344,X345,X346,X347)) )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X347 = esk2_4(X344,X345,X346,X347)
| X347 = hAPP(list(char),ty,class,esk4_4(X344,X345,X346,X347))
| X346 = nt )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X347 = esk2_4(X344,X345,X346,X347)
| X346 = hAPP(list(char),ty,class,esk3_4(X344,X345,X346,X347))
| X347 = hAPP(list(char),ty,class,esk5_4(X344,X345,X346,X347)) )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X347 = esk2_4(X344,X345,X346,X347)
| X346 = hAPP(list(char),ty,class,esk3_4(X344,X345,X346,X347))
| X346 = nt )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X346 = esk2_4(X344,X345,X346,X347)
| hBOOL(hAPP(fun(product_prod(list(char),list(char)),bool),bool,hAPP(product_prod(list(char),list(char)),fun(fun(product_prod(list(char),list(char)),bool),bool),member(product_prod(list(char),list(char))),hAPP(list(char),product_prod(list(char),list(char)),hAPP(list(char),fun(list(char),product_prod(list(char),list(char))),product_Pair(list(char),list(char)),esk3_4(X344,X345,X346,X347)),esk4_4(X344,X345,X346,X347))),hAPP(fun(product_prod(list(char),list(char)),bool),fun(product_prod(list(char),list(char)),bool),transitive_rtrancl(list(char)),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(product_prod(list(char),list(char)),bool),subcls1(X344),X345))))
| X347 = hAPP(list(char),ty,class,esk5_4(X344,X345,X346,X347)) )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X346 = esk2_4(X344,X345,X346,X347)
| hBOOL(hAPP(fun(product_prod(list(char),list(char)),bool),bool,hAPP(product_prod(list(char),list(char)),fun(fun(product_prod(list(char),list(char)),bool),bool),member(product_prod(list(char),list(char))),hAPP(list(char),product_prod(list(char),list(char)),hAPP(list(char),fun(list(char),product_prod(list(char),list(char))),product_Pair(list(char),list(char)),esk3_4(X344,X345,X346,X347)),esk4_4(X344,X345,X346,X347))),hAPP(fun(product_prod(list(char),list(char)),bool),fun(product_prod(list(char),list(char)),bool),transitive_rtrancl(list(char)),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(product_prod(list(char),list(char)),bool),subcls1(X344),X345))))
| X346 = nt )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X346 = esk2_4(X344,X345,X346,X347)
| X347 = hAPP(list(char),ty,class,esk4_4(X344,X345,X346,X347))
| X347 = hAPP(list(char),ty,class,esk5_4(X344,X345,X346,X347)) )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X346 = esk2_4(X344,X345,X346,X347)
| X347 = hAPP(list(char),ty,class,esk4_4(X344,X345,X346,X347))
| X346 = nt )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X346 = esk2_4(X344,X345,X346,X347)
| X346 = hAPP(list(char),ty,class,esk3_4(X344,X345,X346,X347))
| X347 = hAPP(list(char),ty,class,esk5_4(X344,X345,X346,X347)) )
& ( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X344)))))))),fun(ty,fun(ty,bool)),widen(X344),X345),X346),X347))
| X346 = esk2_4(X344,X345,X346,X347)
| X346 = hAPP(list(char),ty,class,esk3_4(X344,X345,X346,X347))
| X346 = nt ) ),
inference(distribute,[status(thm)],[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)],[fact_606_widen_Osimps])])])])])])]) ).
cnf(c_0_8,plain,
( ~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),ha),e),ea),X1))
| hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(ty,fun(ty,bool)),widen(product_prod(list(list(char)),exp(list(char)))),p),esk62_1(X1)),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),ha),e),ea),nt)),
inference(split_conjunct,[status(thm)],[fact_0__096P_ME_Mh_A_092_060turnstile_062_Ae_A_058_ANT_096]) ).
fof(c_0_10,plain,
! [X332] : nt != hAPP(list(char),ty,class,X332),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
fof(c_0_11,negated_conjecture,
~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),nt)),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_12,plain,
( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X2)))))))),fun(ty,fun(ty,bool)),widen(X2),X3),X4),X1))
| X1 = esk2_4(X2,X3,X4,X1)
| X1 = hAPP(list(char),ty,class,esk4_4(X2,X3,X4,X1))
| X1 = hAPP(list(char),ty,class,esk5_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(ty,fun(ty,bool)),widen(product_prod(list(list(char)),exp(list(char)))),p),esk62_1(nt)),nt)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
nt != hAPP(list(char),ty,class,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),nt)),
inference(fof_simplification,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ hBOOL(hAPP(ty,bool,hAPP(ty,fun(ty,bool),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,X2)))))))),fun(ty,fun(ty,bool)),widen(X2),X3),X4),X1))
| X4 = esk2_4(X2,X3,X4,X1)
| X1 = hAPP(list(char),ty,class,esk4_4(X2,X3,X4,X1))
| X1 = hAPP(list(char),ty,class,esk5_4(X2,X3,X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
esk2_4(product_prod(list(list(char)),exp(list(char))),p,esk62_1(nt),nt) = nt,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_14]) ).
fof(c_0_18,negated_conjecture,
~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),nt)),
inference(fof_nnf,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
( ~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),ha),e),ea),X1))
| hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),esk62_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_20,plain,
esk62_1(nt) = nt,
inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_13]),c_0_14]),c_0_14]),c_0_17]) ).
cnf(c_0_21,negated_conjecture,
~ hBOOL(hAPP(ty,bool,hAPP(exp(list(char)),fun(ty,bool),hAPP(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)),hAPP(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool))),hAPP(list(product_prod(list(char),product_prod(list(char),product_prod(list(product_prod(list(char),ty)),list(product_prod(list(char),product_prod(list(ty),product_prod(ty,product_prod(list(list(char)),exp(list(char))))))))))),fun(fun(nat,option(product_prod(list(char),fun(product_prod(list(char),list(char)),option(val))))),fun(fun(list(char),option(ty)),fun(exp(list(char)),fun(ty,bool)))),wTrt,p),h_a),e),e_a),nt)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_9]),c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW477+7 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.09 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.50 % Computer : n009.cluster.edu
% 0.22/5.50 % Model : x86_64 x86_64
% 0.22/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.50 % Memory : 8046.5625MB
% 0.22/5.50 % OS : Linux 6.8.0-71-generic
% 0.22/5.50 % CPULimit : 300
% 0.22/5.50 % WCLimit : 300
% 0.22/5.50 % DateTime : Mon Sep 21 10:01:47 UTC 2026
% 0.22/5.51 % CPUTime :
% 0.22/5.51 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.57 Running first-order theorem proving
% 0.22/5.57 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
% 24.09/10.10 % Version: 3.5.1
% 24.09/10.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 24.09/10.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.09/10.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 24.09/10.10 % Starting new_bool_3 with 300s (1) cores
% 24.09/10.10 % Starting new_bool_1 with 300s (1) cores
% 24.09/10.10 % Starting sh5l with 300s (1) cores
% 24.09/10.10 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1467818 completed with status 0
% 24.09/10.10 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 24.09/10.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 24.09/10.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.09/10.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 24.09/10.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.09/10.10 % SinE strategy is gf200_h_gu_R03_F100_L20000
% 24.09/10.10 % Search class: FGHSM-SSLM33-DFFFFFNN
% 24.09/10.10 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 24.09/10.10 % Starting SubtermCWHack with 136s (1) cores
% 24.09/10.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 24.09/10.10 % Starting G-E--_008_C45_F1_PI_S5PRR_SE_Q4_CS_SP_S4S with 226s (1) cores
% 24.09/10.10 % Starting new_bool_3 with 226s (1) cores
% 24.09/10.10 % Starting new_bool_1 with 226s (1) cores
% 24.09/10.10 % new_bool_3 with pid 1467825 completed with status 0
% 24.09/10.10 % Result found by new_bool_3
% 24.09/10.10 % Preprocessing class: FMLMSMSMSSSNFFN.
% 24.09/10.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 24.09/10.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 24.09/10.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 24.09/10.10 % SinE strategy is gf200_h_gu_R03_F100_L20000
% 24.09/10.10 % Search class: FGHSM-SSLM33-DFFFFFNN
% 24.09/10.10 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 24.09/10.10 % Starting SubtermCWHack with 136s (1) cores
% 24.09/10.10 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 24.09/10.10 % Starting G-E--_008_C45_F1_PI_S5PRR_SE_Q4_CS_SP_S4S with 226s (1) cores
% 24.09/10.10 % Starting new_bool_3 with 226s (1) cores
% 24.09/10.10 % Preprocessing time : 0.108 s
% 24.09/10.10 % Presaturation interreduction done
% 24.09/10.10
% 24.09/10.10 % Proof found!
% 24.09/10.10 % SZS status Theorem
% 24.09/10.10 % SZS output start CNFRefutation
% See solution above
% 24.09/10.10 % Parsed axioms : 1180
% 24.09/10.10 % Removed by relevancy pruning/SinE : 375
% 24.09/10.10 % Initial clauses : 1131
% 24.09/10.10 % Removed in clause preprocessing : 24
% 24.09/10.10 % Initial clauses in saturation : 1107
% 24.09/10.10 % Processed clauses : 4109
% 24.09/10.10 % ...of these trivial : 107
% 24.09/10.10 % ...subsumed : 2176
% 24.09/10.10 % ...remaining for further processing : 1826
% 24.09/10.10 % Other redundant clauses eliminated : 402
% 24.09/10.10 % Clauses deleted for lack of memory : 0
% 24.09/10.10 % Backward-subsumed : 34
% 24.09/10.10 % Backward-rewritten : 24
% 24.09/10.10 % Generated clauses : 13407
% 24.09/10.10 % ...of the previous two non-redundant : 11329
% 24.09/10.10 % ...aggressively subsumed : 0
% 24.09/10.10 % Contextual simplify-reflections : 11
% 24.09/10.10 % Paramodulations : 12911
% 24.09/10.10 % Factorizations : 18
% 24.09/10.10 % NegExts : 0
% 24.09/10.10 % Equation resolutions : 493
% 24.09/10.10 % Disequality decompositions : 0
% 24.09/10.10 % Total rewrite steps : 4473
% 24.09/10.10 % ...of those cached : 3326
% 24.09/10.10 % Propositional unsat checks : 0
% 24.09/10.10 % Propositional check models : 0
% 24.09/10.10 % Propositional check unsatisfiable : 0
% 24.09/10.10 % Propositional clauses : 0
% 24.09/10.10 % Propositional clauses after purity: 0
% 24.09/10.10 % Propositional unsat core size : 0
% 24.09/10.10 % Propositional preprocessing time : 0.000
% 24.09/10.10 % Propositional encoding time : 0.000
% 24.09/10.10 % Propositional solver time : 0.000
% 24.09/10.10 % Success case prop preproc time : 0.000
% 24.09/10.10 % Success case prop encoding time : 0.000
% 24.09/10.10 % Success case prop solver time : 0.000
% 24.09/10.10 % Current number of processed clauses : 778
% 24.09/10.11 % Positive orientable unit clauses : 213
% 24.09/10.11 % Positive unorientable unit clauses: 4
% 24.09/10.11 % Negative unit clauses : 118
% 24.09/10.11 % Non-unit-clauses : 443
% 24.09/10.11 % Current number of unprocessed clauses: 9134
% 24.09/10.11 % ...number of literals in the above : 31822
% 24.09/10.11 % Current number of archived formulas : 0
% 24.09/10.11 % Current number of archived clauses : 1004
% 24.09/10.11 % Clause-clause subsumption calls (NU) : 267010
% 24.09/10.11 % Rec. Clause-clause subsumption calls : 101525
% 24.09/10.11 % Non-unit clause-clause subsumptions : 1614
% 24.09/10.11 % Unit Clause-clause subsumption calls : 1724
% 24.09/10.11 % Rewrite failures with RHS unbound : 0
% 24.09/10.11 % BW rewrite match attempts : 11253
% 24.09/10.11 % BW rewrite match successes : 20
% 24.09/10.11 % Condensation attempts : 0
% 24.09/10.11 % Condensation successes : 0
% 24.09/10.11 % Termbank termtop insertions : 3658356
% 24.09/10.11 % Search garbage collected termcells : 24403
% 24.09/10.11
% 24.09/10.11 % -------------------------------------------------
% 24.09/10.11 % User time : 2.050 s
% 24.09/10.11 % System time : 0.070 s
% 24.09/10.11 % Total time : 2.120 s
% 24.09/10.11 % Maximum resident set size: 12740 pages
% 24.09/10.11
% 24.09/10.11 % -------------------------------------------------
% 24.09/10.11 % User time : 13.486 s
% 24.09/10.11 % System time : 0.406 s
% 24.09/10.11 % Total time : 13.892 s
% 24.09/10.11 % Maximum resident set size: 7424 pages
% 24.09/10.11 % E exiting
%------------------------------------------------------------------------------