%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925+8 : 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 : n017.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 01:51:03 PM UTC 2026
% Result : Theorem 122.94s 19.15s
% Output : CNFRefutation 122.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 23
% Syntax : Number of formulae : 82 ( 71 unt; 0 def)
% Number of atoms : 112 ( 81 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 60 ( 30 ~; 20 |; 2 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 12 con; 0-4 aty)
% Number of variables : 96 ( 3 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_2924_succ__pred,axiom,
! [X11] : hAPP(int,int,succ,hAPP(int,int,pred,X11)) = ti(int,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2924_succ__pred) ).
fof(help_COMBI_1_1_U,axiom,
! [X1,X230] : hAPP(X1,X1,combi(X1),X230) = ti(X1,X230),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
fof(fact_123_number__of__is__id,axiom,
! [X21] : hAPP(int,int,number_number_of(int),X21) = ti(int,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_number__of__is__id) ).
fof(fact_742_diff__bin__simps_I1_J,axiom,
! [X21] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X21),pls) = ti(int,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_742_diff__bin__simps_I1_J) ).
fof(fact_2926_pred__Bit1,axiom,
! [X21] : hAPP(int,int,pred,hAPP(int,int,bit1,X21)) = hAPP(int,int,bit0,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2926_pred__Bit1) ).
fof(fact_168_field__power__not__zero,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X16,X37] :
( ti(X1,X37) != zero_zero(X1)
=> hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X37),X16) != zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_field__power__not__zero) ).
fof(conj_0,conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_1004_nat__number__of__def,axiom,
! [X10] : hAPP(int,nat,number_number_of(nat),X10) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1004_nat__number__of__def) ).
fof(fact_4285_card__atLeastZeroLessThan__int,axiom,
! [X80] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X80)) = hAPP(int,nat,nat_1,X80),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4285_card__atLeastZeroLessThan__int) ).
fof(fact_534_not__less__iff__gr__or__eq,axiom,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( ti(X1,X6) = ti(X1,X7)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_not__less__iff__gr__or__eq) ).
fof(fact_1450_int__Suc,axiom,
! [X15] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X15)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1450_int__Suc) ).
fof(fact_37_one__is__num__one,axiom,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(fact_72_Bit0__Pls,axiom,
hAPP(int,int,bit0,pls) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
fof(fact_284_succ__Pls,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_succ__Pls) ).
fof(tsy_c_hAPP_res,axiom,
! [X2,X1,X4,X5] : ti(X2,hAPP(X1,X2,X4,X5)) = hAPP(X1,X2,X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(fact_76_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Pls__def) ).
fof(fact_4286_card__atLeastLessThan__int,axiom,
! [X14,X80] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X14),X80)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X80),X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4286_card__atLeastLessThan__int) ).
fof(fact_21_int__power,axiom,
! [X15,X16] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X15),X16)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X15)),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_int__power) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(fact_2928_pred__Pls,axiom,
hAPP(int,int,pred,pls) = min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2928_pred__Pls) ).
fof(fact_686_succ__Min,axiom,
hAPP(int,int,succ,min) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_succ__Min) ).
fof(arity_Int_Oint___Orderings_Olinorder,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
fof(c_0_23,plain,
! [X7308] : hAPP(int,int,succ,hAPP(int,int,pred,X7308)) = ti(int,X7308),
inference(variable_rename,[status(thm)],[fact_2924_succ__pred]) ).
fof(c_0_24,plain,
! [X13894,X13895] : hAPP(X13894,X13894,combi(X13894),X13895) = ti(X13894,X13895),
inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).
fof(c_0_25,plain,
! [X585] : hAPP(int,int,number_number_of(int),X585) = ti(int,X585),
inference(variable_rename,[status(thm)],[fact_123_number__of__is__id]) ).
cnf(c_0_26,plain,
hAPP(int,int,succ,hAPP(int,int,pred,X1)) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_29,plain,
! [X2216] : hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2216),pls) = ti(int,X2216),
inference(variable_rename,[status(thm)],[fact_742_diff__bin__simps_I1_J]) ).
cnf(c_0_30,plain,
hAPP(int,int,succ,hAPP(int,int,pred,X1)) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_28,c_0_27]) ).
fof(c_0_32,plain,
! [X7310] : hAPP(int,int,pred,hAPP(int,int,bit1,X7310)) = hAPP(int,int,bit0,X7310),
inference(variable_rename,[status(thm)],[fact_2926_pred__Bit1]) ).
fof(c_0_33,plain,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X16,X37] :
( ti(X1,X37) != zero_zero(X1)
=> hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X37),X16) != zero_zero(X1) ) ),
inference(fof_simplification,[status(thm)],[fact_168_field__power__not__zero]) ).
fof(c_0_34,negated_conjecture,
~ ( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_35,plain,
! [X2961] : hAPP(int,nat,number_number_of(nat),X2961) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X2961)),
inference(variable_rename,[status(thm)],[fact_1004_nat__number__of__def]) ).
fof(c_0_36,plain,
! [X11051] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X11051)) = hAPP(int,nat,nat_1,X11051),
inference(variable_rename,[status(thm)],[fact_4285_card__atLeastZeroLessThan__int]) ).
cnf(c_0_37,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),pls) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_38,plain,
! [X1] :
( linorder(X1)
=> ! [X6,X7] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X7))
<=> ( ti(X1,X6) = ti(X1,X7)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X7),X6)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_534_not__less__iff__gr__or__eq]) ).
fof(c_0_39,plain,
! [X4003] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X4003)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X4003)),
inference(variable_rename,[status(thm)],[fact_1450_int__Suc]) ).
cnf(c_0_40,plain,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_37_one__is__num__one]) ).
cnf(c_0_41,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_42,plain,
hAPP(int,int,pred,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,X1),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,plain,
hAPP(int,int,bit0,pls) = pls,
inference(split_conjunct,[status(thm)],[fact_72_Bit0__Pls]) ).
cnf(c_0_44,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_284_succ__Pls]) ).
fof(c_0_45,plain,
! [X681,X682,X683] :
( hAPP(nat,X681,hAPP(X681,fun(nat,X681),power_power(X681),X683),X682) != zero_zero(X681)
| ti(X681,X683) = zero_zero(X681)
| ~ ring_11004092258visors(X681) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
fof(c_0_46,plain,
! [X390,X391,X392,X393] : ti(X390,hAPP(X391,X390,X392,X393)) = hAPP(X391,X390,X392,X393),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
fof(c_0_47,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
cnf(c_0_48,plain,
hAPP(int,nat,number_number_of(nat),X1) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),X1)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),X1)) = hAPP(int,nat,nat_1,X1),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_76_Pls__def]) ).
fof(c_0_51,plain,
! [X11052,X11053] : hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X11052),X11053)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X11053),X11052)),
inference(variable_rename,[status(thm)],[fact_4286_card__atLeastLessThan__int]) ).
cnf(c_0_52,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),pls) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_37,c_0_27]) ).
fof(c_0_53,plain,
! [X1735,X1736,X1737] :
( ( ~ linorder(X1735)
| ~ hBOOL(hAPP(X1735,bool,hAPP(X1735,fun(X1735,bool),ord_less(X1735),X1736),X1737))
| ti(X1735,X1736) != ti(X1735,X1737) )
& ( ~ linorder(X1735)
| ~ hBOOL(hAPP(X1735,bool,hAPP(X1735,fun(X1735,bool),ord_less(X1735),X1736),X1737))
| ~ hBOOL(hAPP(X1735,bool,hAPP(X1735,fun(X1735,bool),ord_less(X1735),X1737),X1736)) )
& ( ~ linorder(X1735)
| ti(X1735,X1736) = ti(X1735,X1737)
| hBOOL(hAPP(X1735,bool,hAPP(X1735,fun(X1735,bool),ord_less(X1735),X1737),X1736))
| hBOOL(hAPP(X1735,bool,hAPP(X1735,fun(X1735,bool),ord_less(X1735),X1736),X1737)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])]) ).
cnf(c_0_54,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X1)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_55,plain,
one_one(int) = hAPP(int,int,bit1,pls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_56,plain,
( hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_57,plain,
! [X425,X426] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X425),X426)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X425)),X426),
inference(variable_rename,[status(thm)],[fact_21_int__power]) ).
cnf(c_0_58,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_59,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_60,plain,
hAPP(int,nat,number_number_of(nat),X1) = hAPP(int,nat,nat_1,hAPP(int,int,succ,hAPP(int,int,pred,X1))),
inference(rw,[status(thm)],[c_0_48,c_0_41]) ).
cnf(c_0_61,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),pls),X1)) = hAPP(int,nat,nat_1,X1),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,plain,
hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),X1),X2)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X2),X1)),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_63,plain,
hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X1),pls) = hAPP(int,int,succ,hAPP(int,int,pred,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_31]),c_0_41]) ).
cnf(c_0_64,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_65,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_66,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X1)),
inference(rw,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_67,plain,
( ~ ring_11004092258visors(X1)
| hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1)
| hAPP(X1,X1,combi(X1),X2) = zero_zero(X1) ),
inference(rw,[status(thm)],[c_0_56,c_0_27]) ).
cnf(c_0_68,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1),X2)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_69,plain,
hAPP(X1,X1,combi(X1),hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(rw,[status(thm)],[c_0_58,c_0_27]) ).
cnf(c_0_70,plain,
ring_11004092258visors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
cnf(c_0_71,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,nat_1,hAPP(int,int,succ,hAPP(int,int,pred,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_55]),c_0_60]),c_0_50]) ).
cnf(c_0_72,plain,
hAPP(int,nat,nat_1,hAPP(int,int,succ,hAPP(int,int,pred,X1))) = hAPP(int,nat,nat_1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_73,plain,
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ~ linorder(X1)
| hAPP(X1,X1,combi(X1),X2) != hAPP(X1,X1,combi(X1),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_27]),c_0_27]) ).
cnf(c_0_74,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_50]),c_0_55]),c_0_66]) ).
cnf(c_0_75,plain,
hAPP(int,int,pred,pls) = min,
inference(split_conjunct,[status(thm)],[fact_2928_pred__Pls]) ).
cnf(c_0_76,plain,
hAPP(int,int,succ,min) = pls,
inference(split_conjunct,[status(thm)],[fact_686_succ__Min]) ).
cnf(c_0_77,plain,
linorder(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Olinorder]) ).
cnf(c_0_78,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X1),X2)) != pls
| hAPP(nat,int,semiring_1_of_nat(int),X1) = pls ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_50]),c_0_50]),c_0_70])]) ).
cnf(c_0_79,negated_conjecture,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_66]),c_0_72]),c_0_68]) ).
cnf(c_0_80,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) != pls,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_31]),c_0_41]),c_0_75]),c_0_76]),c_0_69]),c_0_77])]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM925+8 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 03:13:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 122.94/19.15 % Version: 3.5.1
% 122.94/19.15 % Preprocessing class: FMLMSMSLSSSNFFN.
% 122.94/19.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.94/19.15 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 122.94/19.15 % Starting new_bool_3 with 600s (2) cores
% 122.94/19.15 % Starting new_bool_1 with 600s (2) cores
% 122.94/19.15 % Starting sh5l with 300s (1) cores
% 122.94/19.15 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1305397 completed with status 0
% 122.94/19.15 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 122.94/19.15 % Preprocessing class: FMLMSMSLSSSNFFN.
% 122.94/19.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.94/19.15 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 122.94/19.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 122.94/19.15 % No SInE strategy applied
% 122.94/19.15 % Search class: FGHSM-SMLM33-DFFFFFNN
% 122.94/19.15 % Scheduled 7 strats onto 3 cores with 899 seconds (899 total)
% 122.94/19.15 % Starting SubtermCWHack with 81s (1) cores
% 122.94/19.15 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 122.94/19.15 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 81s (1) cores
% 122.94/19.15 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1305407 completed with status 0
% 122.94/19.15 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 122.94/19.15 % Preprocessing class: FMLMSMSLSSSNFFN.
% 122.94/19.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 122.94/19.15 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 122.94/19.15 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 122.94/19.15 % No SInE strategy applied
% 122.94/19.15 % Search class: FGHSM-SMLM33-DFFFFFNN
% 122.94/19.15 % Scheduled 7 strats onto 3 cores with 899 seconds (899 total)
% 122.94/19.15 % Starting SubtermCWHack with 81s (1) cores
% 122.94/19.15 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 122.94/19.15 % Preprocessing time : 0.494 s
% 122.94/19.15 % Presaturation interreduction done
% 122.94/19.15
% 122.94/19.15 % Proof found!
% 122.94/19.15 % SZS status Theorem
% 122.94/19.15 % SZS output start CNFRefutation
% See solution above
% 122.94/19.15 % Parsed axioms : 5747
% 122.94/19.15 % Removed by relevancy pruning/SinE : 0
% 122.94/19.15 % Initial clauses : 8678
% 122.94/19.15 % Removed in clause preprocessing : 213
% 122.94/19.15 % Initial clauses in saturation : 8465
% 122.94/19.15 % Processed clauses : 15791
% 122.94/19.15 % ...of these trivial : 412
% 122.94/19.15 % ...subsumed : 5004
% 122.94/19.15 % ...remaining for further processing : 10375
% 122.94/19.15 % Other redundant clauses eliminated : 395
% 122.94/19.15 % Clauses deleted for lack of memory : 0
% 122.94/19.15 % Backward-subsumed : 192
% 122.94/19.15 % Backward-rewritten : 391
% 122.94/19.15 % Generated clauses : 16849
% 122.94/19.15 % ...of the previous two non-redundant : 13581
% 122.94/19.15 % ...aggressively subsumed : 0
% 122.94/19.15 % Contextual simplify-reflections : 26
% 122.94/19.15 % Paramodulations : 16459
% 122.94/19.15 % Factorizations : 5
% 122.94/19.15 % NegExts : 0
% 122.94/19.15 % Equation resolutions : 406
% 122.94/19.15 % Disequality decompositions : 0
% 122.94/19.15 % Total rewrite steps : 32981
% 122.94/19.15 % ...of those cached : 29592
% 122.94/19.15 % Propositional unsat checks : 3
% 122.94/19.15 % Propositional check models : 2
% 122.94/19.15 % Propositional check unsatisfiable : 0
% 122.94/19.15 % Propositional clauses : 0
% 122.94/19.15 % Propositional clauses after purity: 0
% 122.94/19.15 % Propositional unsat core size : 0
% 122.94/19.15 % Propositional preprocessing time : 0.000
% 122.94/19.15 % Propositional encoding time : 0.239
% 122.94/19.15 % Propositional solver time : 0.090
% 122.94/19.15 % Success case prop preproc time : 0.000
% 122.94/19.15 % Success case prop encoding time : 0.000
% 122.94/19.15 % Success case prop solver time : 0.000
% 122.94/19.15 % Current number of processed clauses : 2272
% 122.94/19.15 % Positive orientable unit clauses : 1298
% 122.94/19.15 % Positive unorientable unit clauses: 0
% 122.94/19.15 % Negative unit clauses : 164
% 122.94/19.15 % Non-unit-clauses : 810
% 122.94/19.15 % Current number of unprocessed clauses: 13224
% 122.94/19.15 % ...number of literals in the above : 33029
% 122.94/19.15 % Current number of archived formulas : 0
% 122.94/19.15 % Current number of archived clauses : 7798
% 122.94/19.15 % Clause-clause subsumption calls (NU) : 8362496
% 122.94/19.15 % Rec. Clause-clause subsumption calls : 1646492
% 122.94/19.15 % Non-unit clause-clause subsumptions : 2149
% 122.94/19.15 % Unit Clause-clause subsumption calls : 6845
% 122.94/19.15 % Rewrite failures with RHS unbound : 0
% 122.94/19.15 % BW rewrite match attempts : 337714
% 122.94/19.15 % BW rewrite match successes : 634
% 122.94/19.15 % Condensation attempts : 0
% 122.94/19.16 % Condensation successes : 0
% 122.94/19.16 % Termbank termtop insertions : 3311849
% 122.94/19.16 % Search garbage collected termcells : 114441
% 122.94/19.16
% 122.94/19.16 % -------------------------------------------------
% 122.94/19.16 % User time : 17.625 s
% 122.94/19.16 % System time : 0.316 s
% 122.94/19.16 % Total time : 17.941 s
% 122.94/19.16 % Maximum resident set size: 45092 pages
% 122.94/19.16
% 122.94/19.16 % -------------------------------------------------
% 122.94/19.16 % User time : 49.031 s
% 122.94/19.16 % System time : 0.995 s
% 122.94/19.16 % Total time : 50.026 s
% 122.94/19.16 % Maximum resident set size: 13056 pages
% 122.94/19.16 % E exiting
%------------------------------------------------------------------------------