%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM925+8 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:58:54 PM UTC 2026
% Result : Theorem 25.05s 15.09s
% Output : CNFRefutation 25.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 66 ( 57 unt; 0 def)
% Number of atoms : 85 ( 65 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 13 |; 3 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 9 con; 0-4 aty)
% Number of variables : 50 ( 2 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_79_add__Pls,axiom,
! [X21] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X21) = ti(int,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_add__Pls) ).
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_29_nat__1__add__1,axiom,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
fof(fact_76_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Pls__def) ).
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(fact_303_succ__def,axiom,
! [X21] : hAPP(int,int,succ,X21) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X21),one_one(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_succ__def) ).
fof(fact_1484_semiring__norm_I115_J,axiom,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1484_semiring__norm_I115_J) ).
fof(fact_1382_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1382_One__nat__def) ).
fof(fact_223_zless__le,axiom,
! [X30,X25] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X30),X25))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X30),X25))
& ti(int,X30) != ti(int,X25) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_zless__le) ).
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_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_3596_of__int__int__eq,axiom,
! [X16] : hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),X16)) = hAPP(nat,int,semiring_1_of_nat(int),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3596_of__int__int__eq) ).
fof(fact_3593_int__number__of__def,axiom,
! [X9] : hAPP(int,int,number_number_of(int),X9) = hAPP(int,int,ring_1_of_int(int),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3593_int__number__of__def) ).
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(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(fact_19_zero__is__num__zero,axiom,
zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
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(c_0_18,plain,
! [X13879] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X13879) = ti(int,X13879),
inference(variable_rename,[status(thm)],[fact_79_add__Pls]) ).
fof(c_0_19,plain,
! [X27263,X27264] : hAPP(X27263,X27263,combi(X27263),X27264) = ti(X27263,X27264),
inference(variable_rename,[status(thm)],[help_COMBI_1_1_U]) ).
fof(c_0_20,plain,
! [X13954] : hAPP(int,int,number_number_of(int),X13954) = ti(int,X13954),
inference(variable_rename,[status(thm)],[fact_123_number__of__is__id]) ).
cnf(c_0_21,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_29_nat__1__add__1]) ).
cnf(c_0_22,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_76_Pls__def]) ).
cnf(c_0_23,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_284_succ__Pls]) ).
fof(c_0_24,plain,
! [X14399] : hAPP(int,int,succ,X14399) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X14399),one_one(int)),
inference(variable_rename,[status(thm)],[fact_303_succ__def]) ).
cnf(c_0_25,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
hAPP(int,int,number_number_of(int),X1) = ti(int,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(split_conjunct,[status(thm)],[fact_1484_semiring__norm_I115_J]) ).
cnf(c_0_29,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,zero_zero(int)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(split_conjunct,[status(thm)],[fact_1382_One__nat__def]) ).
cnf(c_0_31,plain,
hAPP(int,int,succ,zero_zero(int)) = hAPP(int,int,bit1,zero_zero(int)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_22]),c_0_22]) ).
cnf(c_0_32,plain,
hAPP(int,int,succ,X1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X1),one_one(int)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),X1) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,combi(int),X1),
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_35,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat)) = hAPP(nat,nat,suc,one_one(nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_22]),c_0_29]),c_0_30]) ).
cnf(c_0_36,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),one_one(int)) = hAPP(int,int,bit1,zero_zero(int)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),X1) = hAPP(int,int,number_number_of(int),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34]),c_0_22]) ).
fof(c_0_38,plain,
! [X14185,X14186] :
( ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14185),X14186))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14185),X14186)) )
& ( ti(int,X14185) != ti(int,X14186)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14185),X14186)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X14185),X14186))
| ti(int,X14185) = ti(int,X14186)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X14185),X14186)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_223_zless__le])])]) ).
fof(c_0_39,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)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_40,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,zero_zero(int)))) = hAPP(nat,nat,suc,one_one(nat)),
inference(rw,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_41,plain,
hAPP(int,int,bit1,zero_zero(int)) = hAPP(int,int,number_number_of(int),one_one(int)),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( ti(int,X1) != ti(int,X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_43,plain,
! [X17372] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,X17372)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),X17372)),
inference(variable_rename,[status(thm)],[fact_1450_int__Suc]) ).
fof(c_0_44,plain,
! [X22448] : hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),X22448)) = hAPP(nat,int,semiring_1_of_nat(int),X22448),
inference(variable_rename,[status(thm)],[fact_3596_of__int__int__eq]) ).
fof(c_0_45,plain,
! [X22444] : hAPP(int,int,number_number_of(int),X22444) = hAPP(int,int,ring_1_of_int(int),X22444),
inference(variable_rename,[status(thm)],[fact_3593_int__number__of__def]) ).
fof(c_0_46,plain,
! [X14050,X14051,X14052] :
( ~ ring_11004092258visors(X14050)
| ti(X14050,X14052) = zero_zero(X14050)
| hAPP(nat,X14050,hAPP(X14050,fun(nat,X14050),power_power(X14050),X14052),X14051) != zero_zero(X14050) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_168_field__power__not__zero])])]) ).
cnf(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(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,number_number_of(int),one_one(int)))) = hAPP(nat,nat,suc,one_one(nat)),
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( hAPP(int,int,combi(int),X1) != hAPP(int,int,combi(int),X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_26]),c_0_26]) ).
cnf(c_0_50,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_51,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_43]) ).
cnf(c_0_52,plain,
zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
inference(split_conjunct,[status(thm)],[fact_19_zero__is__num__zero]) ).
cnf(c_0_53,plain,
hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,plain,
hAPP(int,int,number_number_of(int),X1) = hAPP(int,int,ring_1_of_int(int),X1),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
( ti(X1,X2) = zero_zero(X1)
| ~ ring_11004092258visors(X1)
| hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_56,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(nat,nat,suc,one_one(nat))) = zero_zero(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_22]),c_0_41]),c_0_48]) ).
cnf(c_0_57,plain,
( hAPP(int,int,number_number_of(int),X1) != hAPP(int,int,number_number_of(int),X2)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X1),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_34]),c_0_34]) ).
cnf(c_0_58,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_59,plain,
hAPP(int,int,number_number_of(int),zero_zero(int)) = zero_zero(int),
inference(rw,[status(thm)],[c_0_52,c_0_22]) ).
cnf(c_0_60,plain,
hAPP(int,int,number_number_of(int),hAPP(nat,int,semiring_1_of_nat(int),X1)) = hAPP(nat,int,semiring_1_of_nat(int),X1),
inference(rw,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_61,plain,
( hAPP(X1,X1,combi(X1),X2) = zero_zero(X1)
| hAPP(nat,X1,hAPP(X1,fun(nat,X1),power_power(X1),X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
inference(rw,[status(thm)],[c_0_55,c_0_26]) ).
cnf(c_0_62,negated_conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) = zero_zero(int),
inference(rw,[status(thm)],[c_0_56,c_0_51]) ).
cnf(c_0_63,plain,
ring_11004092258visors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
cnf(c_0_64,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) != zero_zero(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]),c_0_60]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_34]),c_0_60]),c_0_63])]),c_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925+8 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 01:18:06 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 25.05/15.09 % Version : CSE_E---1.7
% 25.05/15.09 % Problem : theBenchmark.p
% 25.05/15.09 % SZS status Theorem for theBenchmark.p
% 25.05/15.09 % SZS output start CNFRefutation
% See solution above
% 25.16/15.17 % Total time : 12.965s
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