TSTP Solution File: NUM925+2 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : NUM925+2 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 : Fri May 3 02:51:11 EDT 2024
% Result : Theorem 10.14s 2.15s
% Output : CNFRefutation 10.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 46 unt; 0 def)
% Number of atoms : 90 ( 68 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 59 ( 27 ~; 16 |; 12 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 1 sgn 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(f25,axiom,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_semiring__one__add__one__is__two) ).
fof(f71,axiom,
! [X25,X26,X27] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X25),X26)),X27) = hAPP_int_int(plus_plus_int(X25),hAPP_int_int(plus_plus_int(X26),X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zadd__assoc) ).
fof(f72,axiom,
! [X7,X9,X16] : hAPP_int_int(plus_plus_int(X7),hAPP_int_int(plus_plus_int(X9),X16)) = hAPP_int_int(plus_plus_int(X9),hAPP_int_int(plus_plus_int(X7),X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zadd__left__commute) ).
fof(f104,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_Pls__def) ).
fof(f106,axiom,
! [X20] : hAPP_int_int(plus_plus_int(X20),pls) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_add__Pls__right) ).
fof(f107,axiom,
! [X20] : hAPP_int_int(plus_plus_int(pls),X20) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__Pls) ).
fof(f109,axiom,
! [X20] : bit0(X20) = hAPP_int_int(plus_plus_int(X20),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_Bit0__def) ).
fof(f134,axiom,
! [X20] : bit1(X20) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X20)),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_Bit1__def) ).
fof(f291,axiom,
! [X4,X17] :
( zero_zero_int = hAPP_nat_int(power_power_int(X4),X17)
<=> ( zero_zero_nat != X17
& zero_zero_int = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_power__eq__0__iff) ).
fof(f453,axiom,
! [X29,X24] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X29),X24))
<=> ( X24 != X29
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X29),X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_zless__le) ).
fof(f708,conjecture,
zero_zero_int != hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f709,negated_conjecture,
~ ( zero_zero_int != hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f708]) ).
fof(f747,plain,
! [X0,X1,X2] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
inference(rectify,[],[f71]) ).
fof(f748,plain,
! [X0,X1,X2] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
inference(rectify,[],[f72]) ).
fof(f777,plain,
! [X0] : hAPP_int_int(plus_plus_int(X0),pls) = X0,
inference(rectify,[],[f106]) ).
fof(f778,plain,
! [X0] : hAPP_int_int(plus_plus_int(pls),X0) = X0,
inference(rectify,[],[f107]) ).
fof(f780,plain,
! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
inference(rectify,[],[f109]) ).
fof(f798,plain,
! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
inference(rectify,[],[f134]) ).
fof(f928,plain,
! [X0,X1] :
( zero_zero_int = hAPP_nat_int(power_power_int(X0),X1)
<=> ( zero_zero_nat != X1
& zero_zero_int = X0 ) ),
inference(rectify,[],[f291]) ).
fof(f1082,plain,
! [X0,X1] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
<=> ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) ) ),
inference(rectify,[],[f453]) ).
fof(f1326,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(flattening,[],[f709]) ).
fof(f1857,plain,
! [X0,X1] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(X0),X1)
| zero_zero_nat = X1
| zero_zero_int != X0 )
& ( ( zero_zero_nat != X1
& zero_zero_int = X0 )
| zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ) ),
inference(nnf_transformation,[],[f928]) ).
fof(f1858,plain,
! [X0,X1] :
( ( zero_zero_int = hAPP_nat_int(power_power_int(X0),X1)
| zero_zero_nat = X1
| zero_zero_int != X0 )
& ( ( zero_zero_nat != X1
& zero_zero_int = X0 )
| zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ) ),
inference(flattening,[],[f1857]) ).
fof(f1913,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(nnf_transformation,[],[f1082]) ).
fof(f1914,plain,
! [X0,X1] :
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1))
| X0 = X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
& ( ( X0 != X1
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X0),X1)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ) ),
inference(flattening,[],[f1913]) ).
fof(f2033,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f6]) ).
fof(f2058,plain,
number_number_of_nat(bit0(bit1(pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(cnf_transformation,[],[f25]) ).
fof(f2126,plain,
! [X2,X0,X1] : hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
inference(cnf_transformation,[],[f747]) ).
fof(f2127,plain,
! [X2,X0,X1] : hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
inference(cnf_transformation,[],[f748]) ).
fof(f2182,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f104]) ).
fof(f2184,plain,
! [X0] : hAPP_int_int(plus_plus_int(X0),pls) = X0,
inference(cnf_transformation,[],[f777]) ).
fof(f2185,plain,
! [X0] : hAPP_int_int(plus_plus_int(pls),X0) = X0,
inference(cnf_transformation,[],[f778]) ).
fof(f2187,plain,
! [X0] : bit0(X0) = hAPP_int_int(plus_plus_int(X0),X0),
inference(cnf_transformation,[],[f780]) ).
fof(f2218,plain,
! [X0] : bit1(X0) = hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),X0)),X0),
inference(cnf_transformation,[],[f798]) ).
fof(f2439,plain,
! [X0,X1] :
( zero_zero_int = X0
| zero_zero_int != hAPP_nat_int(power_power_int(X0),X1) ),
inference(cnf_transformation,[],[f1858]) ).
fof(f2657,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X1)) ),
inference(cnf_transformation,[],[f1914]) ).
fof(f3013,plain,
zero_zero_int = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(cnf_transformation,[],[f1326]) ).
fof(f3014,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(definition_unfolding,[],[f2033,f2182]) ).
fof(f3038,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat) = number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))),
inference(definition_unfolding,[],[f2058,f2187,f2218]) ).
fof(f3169,plain,
! [X0,X1] :
( pls = X0
| pls != hAPP_nat_int(power_power_int(X0),X1) ),
inference(definition_unfolding,[],[f2439,f2182,f2182]) ).
fof(f3339,plain,
pls = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))),
inference(definition_unfolding,[],[f3013,f2182,f2187,f2218]) ).
fof(f3430,plain,
! [X1] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X1),X1)),
inference(equality_resolution,[],[f2657]) ).
cnf(c_54,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f3014]) ).
cnf(c_79,plain,
number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(cnf_transformation,[],[f3038]) ).
cnf(c_137,plain,
hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(X0),X1)),X2) = hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)),
inference(cnf_transformation,[],[f2126]) ).
cnf(c_138,plain,
hAPP_int_int(plus_plus_int(X0),hAPP_int_int(plus_plus_int(X1),X2)) = hAPP_int_int(plus_plus_int(X1),hAPP_int_int(plus_plus_int(X0),X2)),
inference(cnf_transformation,[],[f2127]) ).
cnf(c_193,plain,
hAPP_int_int(plus_plus_int(X0),pls) = X0,
inference(cnf_transformation,[],[f2184]) ).
cnf(c_194,plain,
hAPP_int_int(plus_plus_int(pls),X0) = X0,
inference(cnf_transformation,[],[f2185]) ).
cnf(c_435,plain,
( hAPP_nat_int(power_power_int(X0),X1) != pls
| X0 = pls ),
inference(cnf_transformation,[],[f3169]) ).
cnf(c_633,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X0)),
inference(cnf_transformation,[],[f3430]) ).
cnf(c_969,negated_conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)),hAPP_int_int(plus_plus_int(hAPP_int_int(plus_plus_int(one_one_int),pls)),pls)))) = pls,
inference(cnf_transformation,[],[f3339]) ).
cnf(c_980,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(instantiation,[status(thm)],[c_633]) ).
cnf(c_6744,plain,
number_number_of_nat(hAPP_int_int(plus_plus_int(one_one_int),one_one_int)) = hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat),
inference(demodulation,[status(thm)],[c_79,c_137,c_138,c_193,c_194]) ).
cnf(c_7078,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(plus_plus_nat(one_one_nat),one_one_nat)) = pls,
inference(demodulation,[status(thm)],[c_969,c_137,c_138,c_193,c_194,c_6744]) ).
cnf(c_20162,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(superposition,[status(thm)],[c_7078,c_435]) ).
cnf(c_20167,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(demodulation,[status(thm)],[c_54,c_20162]) ).
cnf(c_20169,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20167,c_980]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : NUM925+2 : TPTP v8.1.2. Released v5.3.0.
% 0.09/0.12 % Command : run_iprover %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 2 19:57:06 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.45 Running first-order theorem proving
% 0.17/0.45 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.14/2.15 % SZS status Started for theBenchmark.p
% 10.14/2.15 % SZS status Theorem for theBenchmark.p
% 10.14/2.15
% 10.14/2.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.14/2.15
% 10.14/2.15 ------ iProver source info
% 10.14/2.15
% 10.14/2.15 git: date: 2024-05-02 19:28:25 +0000
% 10.14/2.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 10.14/2.15 git: non_committed_changes: false
% 10.14/2.15
% 10.14/2.15 ------ Parsing...
% 10.14/2.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.14/2.15
% 10.14/2.15 ------ Preprocessing... sup_sim: 162 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 10.14/2.15
% 10.14/2.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.14/2.15
% 10.14/2.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.14/2.15 ------ Proving...
% 10.14/2.15 ------ Problem Properties
% 10.14/2.15
% 10.14/2.15
% 10.14/2.15 clauses 487
% 10.14/2.15 conjectures 0
% 10.14/2.15 EPR 6
% 10.14/2.15 Horn 425
% 10.14/2.15 unary 128
% 10.14/2.15 binary 232
% 10.14/2.15 lits 999
% 10.14/2.15 lits eq 223
% 10.14/2.15 fd_pure 0
% 10.14/2.15 fd_pseudo 0
% 10.14/2.15 fd_cond 39
% 10.14/2.15 fd_pseudo_cond 29
% 10.14/2.15 AC symbols 0
% 10.14/2.15
% 10.14/2.15 ------ Input Options Time Limit: Unbounded
% 10.14/2.15
% 10.14/2.15
% 10.14/2.15 ------
% 10.14/2.15 Current options:
% 10.14/2.15 ------
% 10.14/2.15
% 10.14/2.15
% 10.14/2.15
% 10.14/2.15
% 10.14/2.15 ------ Proving...
% 10.14/2.15
% 10.14/2.15
% 10.14/2.15 % SZS status Theorem for theBenchmark.p
% 10.14/2.15
% 10.14/2.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.14/2.15
% 10.14/2.15
%------------------------------------------------------------------------------