%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM925+1 : 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 : n014.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 04:58:53 PM UTC 2026
% Result : Theorem 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 45 unt; 0 def)
% Number of atoms : 59 ( 51 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 6 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_83_Bit0__def,axiom,
! [X19] : bit0(X19) = plus_plus_int(X19,X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
fof(fact_99_Bit1__def,axiom,
! [X19] : bit1(X19) = plus_plus_int(plus_plus_int(one_one_int,X19),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
fof(fact_84_zadd__0__right,axiom,
! [X15] : plus_plus_int(X15,zero_zero_int) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zadd__0__right) ).
fof(conj_0,conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_13_quartic__square__square,axiom,
! [X6] : power_power_int(power_power_int(X6,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(X6,number_number_of_nat(bit0(bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_quartic__square__square) ).
fof(fact_12_semiring__one__add__one__is__two,axiom,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_semiring__one__add__one__is__two) ).
fof(fact_78_Pls__def,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
fof(fact_5_zero__power2,axiom,
power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__power2) ).
fof(fact_50_zadd__assoc,axiom,
! [X24,X25,X26] : plus_plus_int(plus_plus_int(X24,X25),X26) = plus_plus_int(X24,plus_plus_int(X25,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zadd__assoc) ).
fof(fact_92_power__eq__0__iff__number__of,axiom,
! [X3,X23] :
( power_power_int(X3,number_number_of_nat(X23)) = zero_zero_int
<=> ( X3 = zero_zero_int
& number_number_of_nat(X23) != zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
fof(fact_62_bin__less__0__simps_I1_J,axiom,
~ ord_less_int(pls,zero_zero_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_bin__less__0__simps_I1_J) ).
fof(fact_0_n1pos,axiom,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(c_0_12,plain,
! [X249] : bit0(X249) = plus_plus_int(X249,X249),
inference(variable_rename,[status(thm)],[fact_83_Bit0__def]) ).
fof(c_0_13,plain,
! [X269] : bit1(X269) = plus_plus_int(plus_plus_int(one_one_int,X269),X269),
inference(variable_rename,[status(thm)],[fact_99_Bit1__def]) ).
fof(c_0_14,plain,
! [X250] : plus_plus_int(X250,zero_zero_int) = X250,
inference(variable_rename,[status(thm)],[fact_84_zadd__0__right]) ).
fof(c_0_15,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
fof(c_0_16,plain,
! [X164] : power_power_int(power_power_int(X164,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(X164,number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(variable_rename,[status(thm)],[fact_13_quartic__square__square]) ).
cnf(c_0_17,plain,
plus_plus_nat(one_one_nat,one_one_nat) = number_number_of_nat(bit0(bit1(pls))),
inference(split_conjunct,[status(thm)],[fact_12_semiring__one__add__one__is__two]) ).
cnf(c_0_18,plain,
bit0(X1) = plus_plus_int(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
bit1(X1) = plus_plus_int(plus_plus_int(one_one_int,X1),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
plus_plus_int(X1,zero_zero_int) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
pls = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_78_Pls__def]) ).
cnf(c_0_22,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
power_power_int(zero_zero_int,number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(split_conjunct,[status(thm)],[fact_5_zero__power2]) ).
cnf(c_0_24,plain,
power_power_int(power_power_int(X1,number_number_of_nat(bit0(bit1(pls)))),number_number_of_nat(bit0(bit1(pls)))) = power_power_int(X1,number_number_of_nat(bit0(bit0(bit1(pls))))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,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_17,c_0_18]),c_0_19]),c_0_19]) ).
cnf(c_0_26,plain,
plus_plus_int(X1,pls) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_27,plain,
! [X209,X210,X211] : plus_plus_int(plus_plus_int(X209,X210),X211) = plus_plus_int(X209,plus_plus_int(X210,X211)),
inference(variable_rename,[status(thm)],[fact_50_zadd__assoc]) ).
cnf(c_0_28,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_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_22,c_0_18]),c_0_19]),c_0_19]) ).
cnf(c_0_29,plain,
power_power_int(zero_zero_int,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_23,c_0_18]),c_0_19]),c_0_19]) ).
fof(c_0_30,plain,
! [X254,X255] :
( ( X254 = zero_zero_int
| power_power_int(X254,number_number_of_nat(X255)) != zero_zero_int )
& ( number_number_of_nat(X255) != zero_zero_nat
| power_power_int(X254,number_number_of_nat(X255)) != zero_zero_int )
& ( X254 != zero_zero_int
| number_number_of_nat(X255) = zero_zero_nat
| power_power_int(X254,number_number_of_nat(X255)) = zero_zero_int ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_92_power__eq__0__iff__number__of])])]) ).
cnf(c_0_31,plain,
power_power_int(power_power_int(X1,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)))),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)))) = power_power_int(X1,number_number_of_nat(plus_plus_int(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)),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)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_32,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_25,c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_33,plain,
plus_plus_int(plus_plus_int(X1,X2),X3) = plus_plus_int(X1,plus_plus_int(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(plus_plus_int(one_one_int,one_one_int))) = pls,
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_26]),c_0_26]),c_0_26]),c_0_26]),c_0_21]) ).
cnf(c_0_35,plain,
power_power_int(pls,number_number_of_nat(plus_plus_int(one_one_int,one_one_int))) = 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_29,c_0_21]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_21]) ).
cnf(c_0_36,plain,
( X1 = zero_zero_int
| power_power_int(X1,number_number_of_nat(X2)) != zero_zero_int ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
power_power_int(power_power_int(X1,plus_plus_nat(one_one_nat,one_one_nat)),plus_plus_nat(one_one_nat,one_one_nat)) = power_power_int(X1,number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int))))),
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(rw,[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(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_31,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_32]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),plus_plus_nat(one_one_nat,one_one_nat)) = pls,
inference(rw,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_39,plain,
power_power_int(pls,plus_plus_nat(one_one_nat,one_one_nat)) = pls,
inference(rw,[status(thm)],[c_0_35,c_0_32]) ).
fof(c_0_40,plain,
~ ord_less_int(pls,zero_zero_int),
inference(fof_simplification,[status(thm)],[fact_62_bin__less__0__simps_I1_J]) ).
cnf(c_0_41,plain,
ord_less_int(zero_zero_int,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_42,plain,
( X1 = pls
| power_power_int(X1,number_number_of_nat(X2)) != pls ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_21]),c_0_21]) ).
cnf(c_0_43,negated_conjecture,
power_power_int(plus_plus_int(one_one_int,semiri1621563631at_int(n)),number_number_of_nat(plus_plus_int(one_one_int,plus_plus_int(one_one_int,plus_plus_int(one_one_int,one_one_int))))) = pls,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_44,plain,
~ ord_less_int(pls,zero_zero_int),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_45,plain,
ord_less_int(pls,plus_plus_int(one_one_int,semiri1621563631at_int(n))),
inference(rw,[status(thm)],[c_0_41,c_0_21]) ).
cnf(c_0_46,negated_conjecture,
plus_plus_int(one_one_int,semiri1621563631at_int(n)) = pls,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
~ ord_less_int(pls,pls),
inference(rw,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_48,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM925+1 : TPTP v9.2.1. Released v5.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n014.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:18:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------