%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM925+5 : TPTP v9.2.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 1.45s 1.77s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 36 unt; 0 def)
% Number of atoms : 60 ( 40 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 12 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 26 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_78_Bit0__def,axiom,
! [X19] : bit0(X19) = plus_plus(int,X19,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
fof(fact_92_Bit1__def,axiom,
! [X19] : bit1(X19) = plus_plus(int,plus_plus(int,one_one(int),X19),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
fof(fact_5_zero__eq__power2,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X6] :
( power_power(X1,X6,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X1)
<=> ti(X1,X6) = zero_zero(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
fof(fact_29_nat__1__add__1,axiom,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
fof(fact_75_add__Pls__right,axiom,
! [X19] : plus_plus(int,X19,pls) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
fof(conj_0,conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_85_add__numeral__0__right,axiom,
! [X1] :
( number_ring(X1)
=> ! [X30] : plus_plus(X1,X30,number_number_of(X1,pls)) = ti(X1,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_add__numeral__0__right) ).
fof(fact_19_zero__is__num__zero,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(arity_Int_Oint___Int_Onumber__ring,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
fof(fact_0_n1pos,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(fact_32_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
fof(c_0_13,plain,
! [X413] : bit0(X413) = plus_plus(int,X413,X413),
inference(variable_rename,[status(thm)],[fact_78_Bit0__def]) ).
fof(c_0_14,plain,
! [X440] : bit1(X440) = plus_plus(int,plus_plus(int,one_one(int),X440),X440),
inference(variable_rename,[status(thm)],[fact_92_Bit1__def]) ).
fof(c_0_15,plain,
! [X311,X312] :
( ( power_power(X311,X312,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(X311)
| ti(X311,X312) = zero_zero(X311)
| ~ ring_11004092258visors(X311) )
& ( ti(X311,X312) != zero_zero(X311)
| power_power(X311,X312,number_number_of(nat,bit0(bit1(pls)))) = zero_zero(X311)
| ~ ring_11004092258visors(X311) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_zero__eq__power2])])])]) ).
cnf(c_0_16,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_29_nat__1__add__1]) ).
cnf(c_0_17,plain,
bit0(X1) = plus_plus(int,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X409] : plus_plus(int,X409,pls) = X409,
inference(variable_rename,[status(thm)],[fact_75_add__Pls__right]) ).
fof(c_0_20,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_21,plain,
( ti(X1,X2) = zero_zero(X1)
| power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))) != zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_18]) ).
cnf(c_0_23,plain,
plus_plus(int,X1,pls) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,plain,
! [X421,X422] :
( ~ number_ring(X421)
| plus_plus(X421,X422,number_number_of(X421,pls)) = ti(X421,X422) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_85_add__numeral__0__right])])]) ).
cnf(c_0_26,plain,
zero_zero(int) = number_number_of(int,pls),
inference(split_conjunct,[status(thm)],[fact_19_zero__is__num__zero]) ).
cnf(c_0_27,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_73_Pls__def]) ).
cnf(c_0_28,plain,
( ti(X1,X2) = zero_zero(X1)
| power_power(X1,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) != zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_17]),c_0_18]),c_0_18]) ).
cnf(c_0_29,plain,
number_number_of(nat,plus_plus(int,one_one(int),one_one(int))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_30,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) = zero_zero(int),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_18]),c_0_18]) ).
cnf(c_0_31,plain,
( plus_plus(X1,X2,number_number_of(X1,pls)) = ti(X1,X2)
| ~ number_ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
number_ring(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Int_Onumber__ring]) ).
cnf(c_0_33,plain,
number_number_of(int,pls) = pls,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_35,plain,
( ti(X1,X2) = zero_zero(X1)
| power_power(X1,X2,plus_plus(nat,one_one(nat),one_one(nat))) != zero_zero(X1)
| ~ ring_11004092258visors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_29]) ).
cnf(c_0_36,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_29]),c_0_27]) ).
cnf(c_0_37,plain,
ti(int,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_23]) ).
cnf(c_0_38,plain,
ring_11004092258visors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
fof(c_0_39,plain,
~ ord_less(int,pls,pls),
inference(fof_simplification,[status(thm)],[fact_32_rel__simps_I2_J]) ).
cnf(c_0_40,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(rw,[status(thm)],[c_0_34,c_0_27]) ).
cnf(c_0_41,negated_conjecture,
plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) = 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_35,c_0_36]),c_0_37]),c_0_27]),c_0_27]),c_0_38])]) ).
cnf(c_0_42,plain,
~ ord_less(int,pls,pls),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925+5 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:19:18 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.45/1.77 % Version : CSE_E---1.7
% 1.45/1.77 % Problem : theBenchmark.p
% 1.45/1.77 % SZS status Theorem for theBenchmark.p
% 1.45/1.77 % SZS output start CNFRefutation
% See solution above
% 1.45/1.77 % Total time : 1.375s
%------------------------------------------------------------------------------